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Show steps for the constant γ

Gamma = Limiting difference between the harmonic series and the natural logarithm

γ table

n1/n(c)
Sum of 1/n
(d)
Ln (n)
γ
(c) - (d)
11101
20.51.50.693147180559950.8069
30.333333333333331.83333333333331.09861228866810.7347
40.252.08333333333331.38629436111990.697
50.22.28333333333331.60943791243410.6739
60.166666666666672.451.79175946922810.6582
70.142857142857142.59285714285711.94591014905530.6469
80.1252.71785714285712.07944154167980.6384
90.111111111111112.82896825396832.19722457733620.6317
100.12.92896825396832.3025850929940.6264
110.0909090909090913.01987734487732.39789527279840.622
120.0833333333333333.10321067821072.4849066497880.6183
130.0769230769230773.18013375513382.56494935746150.6152
140.0714285714285713.25156232656232.63905732961530.6125
150.0666666666666673.3182289932292.70805020110220.6102
160.06253.3807289932292.77258872223980.6081
170.0588235294117653.43955252264082.83321334405620.6063
180.0555555555555563.49510807819632.89037175789620.6047
190.0526315789473683.54773965714372.94443897916640.6033
200.053.59773965714372.9957322735540.602
210.0476190476190483.64535870476273.04452243772340.6008
220.0454545454545453.69081325021733.09104245335830.5998
230.0434782608695653.73429151108683.13549421592910.5988
240.0416666666666673.77595817775353.17805383034790.5979
250.043.81595817775353.21887582486820.5971
260.0384615384615383.8544197162153.25809653802150.5963
270.0370370370370373.89145675325213.29583686600430.5956
280.0357142857142863.92717103896643.33220451017520.595
290.034482758620693.96165379758713.36729582998650.5944
300.0333333333333333.99498713092043.40119738166220.5938
310.0322580645161294.02724519543653.43398720448510.5933
320.031254.05849519543653.46573590279970.5928
330.030303030303034.08879822573963.49650756146650.5923
340.0294117647058824.11820999044543.52636052461620.5918
350.0285714285714294.14678141901693.55534806148940.5914
360.0277777777777784.17455919679463.58351893845610.591
370.0270270270270274.20158622382173.61091791264420.5907
380.0263157894736844.22790201329533.63758615972640.5903
390.0256410256410264.25354303893643.66356164612960.59
400.0254.27854303893643.68887945411390.5897
410.0243902439024394.30293328283883.71357206670430.5894
420.0238095238095244.32674280664833.73766961828340.5891
430.0232558139534884.34999862060183.76120011569360.5888
440.0227272727272734.37272589332913.78418963391830.5885
450.0222222222222224.39494811555133.80666248977030.5883
460.0217391304347834.41668724598613.82864139648910.588
470.0212765957446814.43796384173083.85014760171010.5878
480.0208333333333334.45879717506413.87120101090790.5876
490.0204081632653064.47920533832943.89182029811060.5874
500.024.49920533832943.91202300542810.5872
510.0196078431372554.51881318146673.93182563272430.587
520.0192307692307694.53804395069743.95124371858140.5868
530.0188679245283024.55691187522573.97029191355210.5866
540.0185185185185194.57543039374433.98898404656430.5864
550.0181818181818184.59361221192614.00733318523250.5863
560.0178571428571434.61146935478324.02535169073510.5861
570.0175438596491234.62901321443244.04305126783460.586
580.0172413793103454.64625459374274.06044301054640.5858
590.0169491525423734.66320374628514.07753744390570.5857
600.0166666666666674.67987041295174.09434456222210.5855
610.0163934426229514.69626385557474.11087386417330.5854
620.0161290322580654.71239288783284.12713438504510.5853
630.0158730158730164.72826590370584.14313472639150.5851
640.0156254.74389090370584.15888308335970.585
650.0153846153846154.75927551909044.17438726989560.5849
660.0151515151515154.77442703424194.18965474202640.5848
670.0149253731343284.78935240737624.2046926193910.5847
680.0147058823529414.80405828972924.21950770517610.5846
690.0144927536231884.81855104335244.23410650459730.5844
700.0142857142857144.83283675763814.24849524204940.5843
710.0140845070422544.84692126468034.26267987704130.5842
720.0138888888888894.86081015356924.27666611901610.5841
730.0136986301369864.87450878370624.29045944114840.584
740.0135135135135144.88802229721974.30406509320420.584
750.0133333333333334.9013556305534.31748811353630.5839
760.0131578947368424.91451352528994.33073334028630.5838
770.0129870129870134.92750053827694.34380542185370.5837
780.0128205128205134.94032105109744.35670882668960.5836
790.0126582278481014.95297927894554.3694478524670.5835
800.01254.96547927894554.38202663467390.5835
810.0123456790123464.97782495795794.39444915467240.5834
820.012195121951224.99002007990914.40671924726430.5833
830.0120481927710845.00206827268024.41884060779660.5832
840.0119047619047625.01397303458494.43081679884330.5832
850.0117647058823535.02573774046734.44265125649030.5831
860.0116279069767445.0373656474444.45434729625350.583
870.0114942528735635.04885990031764.46590811865460.583
880.0113636363636365.06022353668124.47733681447820.5829
890.011235955056185.07145949173744.48863636973210.5828
900.0111111111111115.08257060284854.49980967033030.5828
910.0109890109890115.09355961383754.51085950651680.5827
920.0108695652173915.10442917905494.5217885770490.5826
930.0107526881720435.1151818672274.53259949315330.5826
940.010638297872345.12582016509934.543294782270.5825
950.0105263157894745.13634648088884.55387689160050.5825
960.0104166666666675.14676314755544.56434819146780.5824
970.0103092783505155.1570724259064.57471097850340.5824
980.0102040816326535.16727650753864.58496747867060.5823
990.010101010101015.17737751763964.59511985013460.5823
1000.015.18737751763964.60517018598810.5822
1010.00990099009900995.19727850773864.61512051684130.5822
1020.00980392156862755.20708242930734.62497281328430.5821
1030.00970873786407775.21679116717134.63472898822960.5821
1040.00961538461538465.22640655178674.64439089914140.582
1050.00952380952380955.23593036131054.65396035015750.582
1060.00943396226415095.24536432357474.66343909411210.5819
1070.00934579439252345.25471011796724.67282883446190.5819
1080.00925925925925935.26396937722654.68213122712420.5818
1090.00917431192660555.27314368915314.69134788222910.5818
1100.00909090909090915.2822345982444.70048036579240.5818
1110.0090090090090095.2912436072534.70953020131230.5817
1120.00892857142857145.30017217868164.71849887129510.5817
1130.00884955752212395.30902173620374.72738781871230.5816
1140.00877192982456145.31779366602824.73619844839450.5816
1150.0086956521739135.32648931820224.74493212836330.5816
1160.00862068965517245.33511000785734.75359019110640.5815
1170.00854700854700855.34365701640434.76217393479780.5815
1180.00847457627118645.35213159267554.77068462446570.5814
1190.00840336134453785.36053495402014.77912349311150.5814
1200.00833333333333335.36886828735344.7874917427820.5814
1210.00826446280991745.37713275016334.79579054559670.5813
1220.00819672131147545.38532947147484.80402104473330.5813
1230.0081300813008135.39345955277564.81218435537240.5813
1240.00806451612903235.40152406890464.8202815656050.5812
1250.0085.40952406890464.82831373730230.5812
1260.00793650793650795.41746057684114.83628190695150.5812
1270.00787401574803155.42533459258924.84418708645860.5811
1280.00781255.43314709258924.85203026391960.5811
1290.00775193798449615.44089903057374.85981240436170.5811
1300.00769230769230775.4485913382664.86753445045560.5811
1310.00763358778625955.45622492605224.87519732320120.581
1320.00757575757575765.4638006836284.88280192258640.581
1330.00751879699248125.47131948062054.89034912822180.581
1340.00746268656716425.47878216718764.89783979995090.5809
1350.00740740740740745.4861895745954.90527477843840.5809
1360.00735294117647065.49354251577154.91265488573610.5809
1370.00729927007299275.50084178584454.91998092582810.5809
1380.00724637681159425.50808816265614.92725368515720.5808
1390.00719424460431655.51528240726044.93447393313070.5808
1400.00714285714285715.52242526440334.94164242260930.5808
1410.00709219858156035.52951746298484.94875989037820.5808
1420.00704225352112685.5365597165064.95582705760130.5807
1430.0069930069930075.5435527234994.96284463025990.5807
1440.00694444444444445.55049716794344.9698132995760.5807
1450.00689655172413795.55739371966764.97673374242060.5807
1460.00684931506849325.5642430347364.98360662170830.5806
1470.00680272108843545.57104575582454.99043258677870.5806
1480.00675675675675685.57780251258124.99721227376410.5806
1490.00671140939597325.58451392197725.00394630594550.5806
1500.00666666666666675.59118058864395.01063529409630.5805
1510.00662251655629145.59780310520025.01727983681490.5805
1520.00657894736842115.60438205256865.02388052084630.5805
1530.00653594771241835.6109180002815.03043792139240.5805
1540.00649350649350655.61741150677455.03695260241360.5805
1550.00645161290322585.62386311967775.04342511691920.5804
1560.00641025641025645.6302733760885.04985600724950.5804
1570.00636942675159245.63664280283965.05624580534830.5804
1580.00632911392405065.64297191676365.0625950330270.5804
1590.00628930817610065.64926122493975.06890420222020.5804
1600.006255.65551122493975.07517381523380.5803
1610.00621118012422365.6617224050645.08140436498450.5803
1620.00617283950617285.66789524457015.08759633523240.5803
1630.00613496932515345.67403021389535.09375020080680.5803
1640.00609756097560985.68012777487095.09986642782420.5803
1650.00606060606060615.68618838093155.10594547390060.5802
1660.00602409638554225.69221247731715.11198778835650.5802
1670.00598802395209585.69820050126915.11799381241680.5802
1680.0059523809523815.70415288222155.12396397940330.5802
1690.00591715976331365.71007004198485.12989871492310.5802
1700.00588235294117655.7159523949265.13579843705030.5802
1710.00584795321637435.72180034814245.14166355650270.5801
1720.00581395348837215.72761430163085.14749447681350.5801
1730.00578034682080925.73339464845165.15329159449780.5801
1740.00574712643678165.73914177488845.15905529921450.5801
1750.00571428571428575.74485606060265.16478597392350.5801
1760.00568181818181825.75053787878455.17048399503820.5801
1770.00564971751412435.75618759629865.17614973257380.58
1780.00561797752808995.76180557382675.18178355029210.58
1790.00558659217877095.76739216600545.18738580584080.58
1800.00555555555555565.7729477215615.19295685089020.58
1810.0055248618784535.77847258343955.19849703126580.58
1820.00549450549450555.7839670889345.20400668707680.58
1830.00546448087431695.78943156980835.20948615284140.5799
1840.00543478260869575.7948663524175.2149357576090.5799
1850.00540540540540545.80027175782245.22035582507830.5799
1860.00537634408602155.80564810190845.22574667371320.5799
1870.00534759358288775.81099569549135.23110861685460.5799
1880.00531914893617025.81631484442755.23644196282990.5799
1890.00529100529100535.82160584971855.24174701505960.5799
1900.00526315789473685.82686900761325.24702407216050.5798
1910.00523560209424085.83210460970745.25227342804660.5798
1920.00520833333333335.83731294304085.25749537202780.5798
1930.00518134715025915.8424942901915.26269018890490.5798
1940.00515463917525775.84764892936635.26785815906330.5798
1950.00512820512820515.85277713449455.27299955856370.5798
1960.00510204081632655.85787917531085.27811465923050.5798
1970.00507614213197975.86295531744285.2832037287380.5798
1980.00505050505050515.86800582249335.28826703069450.5797
1990.00502512562814075.87303094812145.29330482472450.5797
2000.0055.87803094812145.2983173665480.5797
2010.00497512437810955.88300607249965.30330490805910.5797
2020.0049504950495055.88795656754915.30826769740120.5797
2030.00492610837438425.89288267592345.31320597904180.5797
2040.00490196078431375.89778463670785.31811999384420.5797
2050.00487804878048785.90266268548825.32300997913840.5797
2060.00485436893203885.90751705442035.32787616878960.5796
2070.00483091787439615.91234797229475.33271879326540.5796
2080.00480769230769235.91715566460245.33753807970130.5796
2090.00478468899521535.92194035359765.34233425196480.5796
2100.00476190476190485.92670225835955.34710753071750.5796
2110.0047393364928915.93144159485245.35185813347610.5796
2120.00471698113207555.93615857598455.3565862746720.5796
2130.00469483568075125.94085341166525.36129216570940.5796
2140.00467289719626175.94552630886155.36597601502190.5796
2150.00465116279069775.95017747165225.37063802812770.5795
2160.00462962962962965.95480710128185.37527840768420.5795
2170.00460829493087565.95941539621275.37989735354050.5795
2180.00458715596330285.9640025521765.38449506278910.5795
2190.00456621004566215.96856876222165.38907172981650.5795
2200.00454545454545455.97311421676715.39362754635240.5795
2210.00452488687782815.97763910364495.39816270151780.5795
2220.00450450450450455.98214360814945.40267738187230.5795
2230.00448430493273545.98662791308225.40717177146010.5795
2240.00446428571428575.99109219879645.4116460518550.5794
2250.00444444444444445.99553664324095.41610040220440.5794
2260.00442477876106195.9999614220025.42053499927230.5794
2270.00440528634361236.00436670834565.42495001748140.5794
2280.00438596491228076.00875267325785.42934562895440.5794
2290.00436681222707426.01311948548495.43372200355420.5794
2300.00434782608695656.01746731157195.43807930892320.5794
2310.00432900432900436.02179631590095.44241771052180.5794
2320.00431034482758626.02610666072855.44673737166630.5794
2330.00429184549356226.0303985062225.45103845356570.5794
2340.00427350427350436.03467201049555.45532111535770.5794
2350.00425531914893626.03892732964455.45958551414420.5793
2360.00423728813559326.04316461778015.46383180502560.5793
2370.00421940928270046.04738402706285.46806014113510.5793
2380.00420168067226896.0515857077355.47227067367150.5793
2390.004184100418416.05576980815345.47646355193150.5793
2400.00416666666666676.05993647482015.4806389233420.5793
2410.0041493775933616.06408585241355.48479693349070.5793
2420.00413223140495876.06821808381845.48893772615670.5793
2430.00411522633744866.07233331015595.49306144334050.5793
2440.00409836065573776.07643167081165.49716822529320.5793
2450.00408163265306126.08051330346475.50125821054470.5793
2460.00406504065040656.08457834411515.50533153593240.5792
2470.00404858299595146.0886269271115.5093883366280.5792
2480.00403225806451616.09265918517565.5134287461650.5792
2490.00401606425702816.09667524943265.51745289646470.5792
2500.0046.10067524943265.52146091786220.5792
2510.00398406374501996.10465931317765.52545293913180.5792
2520.0039682539682546.10862756714595.52942908751140.5792
2530.00395256916996056.11258013631585.53338948872750.5792
2540.00393700787401576.11651714418985.53733426701850.5792
2550.0039215686274516.12043871281735.54126354515840.5792
2560.003906256.12434496281735.54517744447960.5792
2570.00389105058365766.12823601340095.54907608489520.5792
2580.00387596899224816.13211198239325.55295958492160.5792
2590.00386100386100396.13597298625425.55682806169950.5791
2600.00384615384615386.13981914010035.56068163101550.5791
2610.00383141762452116.14365055772495.56452040732270.5791
2620.00381679389312986.1474673516185.56834450376110.5791
2630.00380228136882136.15126963298685.57215403217780.5791
2640.00378787878787886.15505751177475.57594910314630.5791
2650.00377358490566046.15883109668045.57972982598620.5791
2660.00375939849624066.16259049517665.58349630878170.5791
2670.00374531835205996.16633581352875.58724865840020.5791
2680.00373134328358216.17006715681225.59098698051090.5791
2690.00371747211895916.17378462893125.59471137960180.5791
2700.00370370370370376.17748833263495.59842195899840.5791
2710.0036900369003696.18117836953535.60211882087970.5791
2720.00367647058823536.18485484012355.6058020662960.5791
2730.00366300366300376.18851784378655.6094717951850.579
2740.00364963503649646.1921674788235.61312810638810.579
2750.00363636363636366.19580384245945.61677109766660.579
2760.00362318840579716.19942703086525.62040086571710.579
2770.00361010830324916.20303713916845.62401750618730.579
2780.00359712230215836.20663426147065.62762111369060.579
2790.0035842293906816.21021849086135.63121178182140.579
2800.00357142857142866.21378991943275.63478960316920.579
2810.003558718861216.21734863829395.63835466933370.579
2820.00354609929078016.22089473758475.64190707093810.579
2830.00353356890459366.22442830648935.64544689764320.579
2840.00352112676056346.22794943324985.64897423816120.579
2850.00350877192982466.23145820517975.65248918026870.579
2860.00349650349650356.23495470867625.65599181081990.579
2870.00348432055749136.23843902923365.65948221575960.579
2880.00347222222222226.24191125145595.66296048013590.579
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