# Find sum of $n$-terms of series [duplicate]

I want to find the sum of a series for which the $n^{th}$ term is given by $T_n=n(n+1)(-1)^{n+1}$ Basically if we find the sum of $n$ terms the series turns out to be like this: $1 \times 2 -2 \times 3 +3 \times 4 -4 \times 5 +5 \times 6\ldots$
If $n=2m$ is even, the sum is $$2(1-3)+4(3-5)+6(5-7)+\cdots+2m((2m-1)-(2m+1)) =2(-2)+4(-2)+\cdots+2m(-2) =-4(1+2+\cdots+m)$$ which I hope is a familiar sum. I'll leave the $n$ odd case to you.