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Sum of the first 10 Square Numbers

Enter n:

Sum of the First
              
Calculate the sum of the first 10 Square Numbers

Σ n Square Numbers formula:

S10  =  n(n + 1)(2n + 1)
  6

S10  =  10(10 + 1)(2(10) + 1)
  6

S10  =  10(11)(20 + 1)
  6

S10  =  10(11)(21)
  6

S10  =  2310
  6






Average (A) of the first 10 Square Numbers

A  =  Sum of the first 10 Square Numbers
  Count

A  =  385
  10






Display the first 10 Square Numbers where Sn denotes the nth number

Sum of the first 10 Square Numbers

  n    Sn  
  1    1  
  2    4  
  3    9  
  4    16  
  5    25  
  6    36  
  7    49  
  8    64  
  9    81  
  10    100  

What is the Answer?

S10 = 385

How does the Sum of the First (n) Numbers Calculator work?

Free Sum of the First (n) Numbers Calculator - Determines the sum of the first (n)
* Whole Numbers
* Natural Numbers
* Even Numbers
* Odd Numbers
* Square Numbers
* Cube Numbers
* Fourth Power Numbers
This calculator has 1 input.

What 7 formulas are used for the Sum of the First (n) Numbers Calculator?

  1. Sum of the first n whole numbers = n(n - 1)/2
  2. Sum of the first n natural numbers = n(n - 1)/2
  3. Sum of the first n even numbers = n(n - 1)
  4. Sum of the first n odd numbers = n2
  5. Sum of the first n square numbers = n(n + 1)(2n + 1)/6
  6. Sum of the first n cube numbers = n2(n + 1)2/4
  7. Sum of the first n fourth power numbers = n(n + 1)(2n + 1)(3n2 + 3n - 1)/30

For more math formulas, check out our Formula Dossier

What 7 concepts are covered in the Sum of the First (n) Numbers Calculator?

even number
a whole number that is able to be divided by two into two equal whole numbers
integer
a whole number; a number that is not a fraction
...,-5,-4,-3,-2,-1,0,1,2,3,4,5,...
natural number
the positive integers (whole numbers)
1, 2, 3, ...
odd number
a whole number that is not able to be divided by two into two equal whole numbers
sum
the total amount resulting from the addition of two or more numbers, amounts, or items
sum of the first (n) numbers
whole number
numbers that include natural numbers and zero
{0, 1, 2, 3, ...}

Example calculations for the Sum of the First (n) Numbers Calculator

  1. sum of the first 9 natural numbers
  2. what is the sum of the first 10 cube numbers
  3. show sum of the first 10 square numbers
  4. sum first 15 even numbers
  5. sum first 18 odd numbers

Sum of the First (n) Numbers Calculator Video


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