r and n are positive integers, r1, n2, and coefficient of (r+2)th term and 3rth term in …

Question

$r$ and $n$ are positive integers, $r>1$, $n>2$, and coefficient of $(r+2)$th term and $3r$th term in the expansion of $(1+x)^{2n}$ are equal, then $n$ equals:

Accepted Answer

${}^{2n}C_{r+1}={}^{2n}C_{3r-1}$ (using 0-indexed term positions). This holds when $r+1+3r-1=2n\Rightarrow4r=2n\Rightarrow n=2r$

Solutions · 1