<s>[INST] Finding partial sum of a series I need to find sum of n terms of series: $$-1 +2-3+4-5+6 .... $$ Which is in the form $$\sum_{k=1}^{n}(-1)^{k}k$$
I am not sure how i should approach this
 [/INST] When $n$ is even, such as $$-1+2-3+4-5+6=\color{red}{-1+1}+1\color{red}{-3+3}+1\color{red}{-5+5}+1=3$$ 
So inductively the total is $$\frac n2$$
When $n$ is odd, such as $$-1+2-3+4-5+6-7=\color{red}{-1+1}+1\color{red}{-3+3}+1\color{red}{-5+5}+1-7=-4$$
So inductively the total is $$-\frac{n+1}{2}$$
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