Statement-1: _ r=0 ^ n (r + 1)^nC_r = (n + 2)2^ n-1 Statement -2: _ r=0 ^ n (r + 1)^nC_rx^r = (1 + x)^n + nx(1 + x)^ n-1 .

JEE Main 2008 Mathematics question

Statement-1: Statement -2: .

(1)Statement −1 is false, Statement −2 is true
(2)Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1Correct
(3)Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.
(4)Statement −1 is true, Statement −2 is false.

Answer: (2)

\sum(r + 1)\binom nrx^r = \sum\binom nrx^r + x\sum r\binom nrx^{r-1} = (1 + x)^n + nx(1 + x)^{n-1} — Statement 2 is

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Question ID VK-039082