If n is even, then the sum of first n terms of the series 1 – 2 + 3 – 4 + 5 – 6 +...,

For even number n,

Consider 1 – 2 + 3 – 4 + 5 – 6 + ................

for 1 – 2 = – 1

3 – 4 = – 1

5 – 6 = –1

i.e Combining two terms at a time given –1

So, if in all, n even terms are there

Sum of the expression $1-2+3-4+$ $n-1-n$

$=-\frac{n}{2}$