[JEE Advanced 1993] prove that sum r 1 k 3 r 1 binom 3n 2r 1 0
Prove that $\sum_{r=1}^{k}(-3)^{r-1}\binom{3n}{2r-1}=0$, where $k=\frac{3n}2$ and $n$ is even.
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
▲ 0
Answer: Proved.
It is the imaginary part of $(1+i\sqrt3)^{3n}=2^{3n}\big(\cos\frac{3n\pi}3+i\sin n\pi\big)$; since $\sin n\pi=0$ for integer $n$, the alternating odd-index sum vanishes.
JEE Advanced 1993 · Binomial Theorem — verified solution by the Vidaara Team.
Log in to post your own answer or join the discussion.
No comments yet — start the discussion.