Question

Hi, MODERATOR and everybody solve this question ,THe value of 1^2+2^2+3^2+.......+n^2 is ????

Answer 1

here we have given a series of natural numbers

1^2 + 2^2 + 3^3 + -----------+ n^2 .

sum of 1^2 + 2^2 + 3^2 + ----+ n^2

= n ( n + 1 ) ( 2 n + 1 ) / 6

Where , n is the last number .

Let us take an example :

Find the sum of

1^2 + 2^2 + 3^2 + ----------+ 10^2 .

Here , we have last term n = 10

Sum = n ( n + 1 ) ( 2n + 1 ) / 6

= 10 ( 10 + 1 ) ( 2 (10 ) + 1 ) / 6

= (10 × 11 × 21 ) / 6

= 770 / 2 = 385 .

therefore,

required sum this series = 385

--------------------------------------------------------