[JEE Main 2008] s 1 sum r 0 n r 1 binom nr n 2 2 n
S-1: $\sum_{r=0}^n(r+1)\binom nr=(n+2)2^{n-1}$. S-2: $\sum_{r=0}^n(r+1)\binom nr x^r=(1+x)^n+nx(1+x)^{n-1}$.
(a) S-1 false, S-2 true
(b) S-1 true, S-2 true; S-2 explains S-1
(c) S-1 true, S-2 true; S-2 not explanation
(d) S-1 true, S-2 false
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
▲ 0
Correct answer: (b) S-1 true, S-2 true; S-2 explains S-1
S-2 is the generating-function identity; setting $x=1$ gives S-1 $=(n+2)2^{n-1}$, so S-2 correctly explains S-1.
JEE Main 2008 · Binomial Theorem — verified solution by the Vidaara Team.
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