Question

find the sum of 1²+2²+3²+...+30²​

Answer 1

In general,

$\bold{ \tiny{ 1^2+2^2+3^2+...+(N−2)^2+(N−1)^2+(N)^2= \frac{N×(N+1)×(2×N+1)}{6} }}$

Here N can be any natural number. It can be proved using Mathematical Induction.

$\small \bold{1^2+2^2+3^2+...+28^2+29^2+30^2}$

Now,

$\bold{ \frac{30 \times (30 + 1) \times (2 \times30 + 1) }{6} = 9455 }$