Question

If C₀, C₁, C₂,......C_n denote the coefficients in the binomial expansion of (1 + x)ⁿ, prove that : C₁ + 2C₂ + 3C₃ +.....+ nC_n = n.2^n–1

i.e. \(\sum\limits_{r =1}^n r.C_r = n.2^{n -1}\)

Answer 1

\(\text{We have}\)