If $c_0, c_1, c_2, \ldots, c_n$ denote the binomial coefficients in the expansion of $(1+x)^n$, then

Question

If $c_0, c_1, c_2, \ldots, c_n$ denote the binomial coefficients in the expansion of $(1+x)^n$, then the value of $c_1+2 c_2+3 c_3+\ldots+n c_n$ is

Professor PC Thomas Classes · Answer

By applying the derivative operator to $(1+x)^n$ and setting $x=1$, we evaluate $\sum k c_k = n 2^{n-1}$.