Statement-1: Σ(r =0->n)(r + 1)nCr = (n + 2)2^(n - 1)

Question

Statement-1: ⁿΣ_{(r =0)}(r + 1)ⁿC_r = (n + 2)2^{n - 1}

Statement-2: ⁿΣ_{(r = 0)}(r + 1)ⁿC_rx^r = (1 + x)n + nx(1 + x)^{n - 1}

(a) Statement-1 is true, Statement-2 is false
(b) Statemen-1 is false, Statement-2 is true
(c) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
(d) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1

Answer 1

Statement-2 is also true & explains Statement-1 also.