i was given the following question:
given n is a positve integer, calculate the given sum: $$ {n \choose 1} -2{n \choose 2} +3{n \choose 3}+ \ldots +(-1)^{n-1}\cdot n {n \choose n} $$
I looked at the expression and it reminds me of Newton's binom.. but i have no idea where to begin.. can someone help me understand how should i approach this?
thank you