I have the sum
$$\sum_{k=0}^{n} \binom{n}{k} k$$
I know the result is $n 2^{n-1}$ but I don't know how you get there. How does one even begin to simplify a sum like this that has binomial coefficients.
I have the sum
$$\sum_{k=0}^{n} \binom{n}{k} k$$
I know the result is $n 2^{n-1}$ but I don't know how you get there. How does one even begin to simplify a sum like this that has binomial coefficients.