Question

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

Answer 1

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