Question

1 sq. +2sq. + 3sq....... n sq.= what is the equation

Answer 1

1² + 2² + 3 ² ........ n² 
The sum of squares of n natural number = $\frac{n(n+1)(2n+1)}{6}$

Answer 2

The given equation 1sq. +2sq. + 3sq....... n sq represents the sum of the square of first n natural numbers and the full equation is given below:

$(1 s q .+2 s q .+3 s q \ldots \ldots \ldots n s q)=\left(1^{2}+2^{2}+3^{2}+\ldots \ldots+n^{2}\right)=\left(\frac{1}{2} n(n+1)(2 n+1)\right)$

Given:

$1^{ 2 }+2^{ 2 }+3^{ 2 }+.......+n^{ 2 }$

To find:

What is the equation = ?

Solution:

$(1 sq.+2 sq.+3 sq.+.......+n sq)=\left(1^{2}+2^{2}+3^{2}+.......+n^{2}\right)$

This equation represents that the sum of the square of first n natural numbers.

And the next half of the equation becomes, $\frac{1}{2} n(n+1)(2 n+1)$

The full equation is,

$(1 sq.+2 sq.+3 sq.+.......+n sq)=\left(1^{2}+2^{2}+3^{2}+.......+n^{2}\right)=\left(\frac{1}{2} n(n+1)(2 n+1)\right)$