Are any of you familiar with the closed form solutions for $\sum_{k=0}^{n} k C(n,k) x^k$ and $\sum_{k=0}^{n} k^2 C(n,k) x^k$ where $0 < x < 1$?
Thanks!
Are any of you familiar with the closed form solutions for $\sum_{k=0}^{n} k C(n,k) x^k$ and $\sum_{k=0}^{n} k^2 C(n,k) x^k$ where $0 < x < 1$?
Thanks!