need help on this one.
used newton's binominal and its derivative but couldnot get the result.
$\displaystyle (1+x)^n = \displaystyle \sum_{k=0}^{k=n} \binom{n}{k}x^k$
differentiate the equation on both the sides:
$\displaystyle n(1+x)^{n-1} = \displaystyle \sum_{k=0}^{k=n} k\binom{n}{k}x^{k-1}$
Multiply by $\displaystyle x$ on both sides:
$\displaystyle nx(1+x)^{n-1} = \displaystyle \sum_{k=0}^{k=n} k\binom{n}{k}x^{k}$
Now substitute $\displaystyle x = -1$ to get your answer