Question

What is the sum of the series $1^2-2^2+3^2-4^2+..+{29}^2-{30}^2$?

Answer 1

We have,

$1^2-2^2+3^2-4^2+....+{29}^2-{30}^2$

We know that the sum of $n$ term in the given series

$S=-\frac{n(n+1)}{2}$

Therefore,

$S=-\frac{30(30+1)}{2}$

$S=-\frac{30\left(31\right)}{2}$

$S=-15\times 31$

$S=-465$

Hence, this is the answer.