[JEE Advanced 1989] prove that c 0 2 2c 1 3 2c 2 1 n n 1
Prove that $C_0-2^2C_1+3^2C_2-\cdots+(-1)^n(n+1)^2C_n=0$ for $n>2$.
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✓ Vidaara Team
✓ Accepted
· 2d ago
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Answer: Proved.
Writing $(r+1)^2=r(r-1)+3r+1$ and using $\sum(-1)^r\binom nr=0$, $\sum(-1)^r r\binom nr=0$, $\sum(-1)^r r(r-1)\binom nr=0$ (all $0$ for $n>2$) gives the result.
JEE Advanced 1989 · Binomial Theorem — verified solution by the Vidaara Team.
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