Write the sum of the series `1^2-2^2+3^2-4^2+5^2-6^2...........+(2n-1)^2-(2n)^2dot`

Explanation

We have given the series `1^2-2^2+3^2-4^2+5^2-6^2...........+(2n-1)^2-(2n)^2`

It can also be write as
`=1−4+9−16+25−`.... to 2n terms

`=(1−4)+(9−16)+(25−36)+`.... to n terms. (after grouping)

`=−3+(−7)+(−11)+....n` terms
As the given series is given in A.P.

hence we have formula of sum of n terms = `n/2(2a(n−1)d)`

Here, `a=-3,d=-4`

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