Suppose A and B are the coefficients of $30^{ ext{th}}$ and $12^{ ext{th}}$ terms respectively in the binomial expansion of $(1+x)^{2n-1}$. If $2A=5B$, then $n$ is equal to :

Question

Suppose A and B are the coefficients of $30^{	ext{th}}$ and $12^{	ext{th}}$ terms respectively in the binomial expansion of $(1+x)^{2n-1}$. If $2A=5B$, then $n$ is equal to :

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] With $N=2n-1$: $A=\binom N{29}$, $B=\binom N{11}$, and $2A=5B$ means $\frac{A}{B}=\frac52$. Using $\frac{\binom N{29}}{\binom N{11}}=\frac{11!\,(N-11)!}{29!\,(N-29)!}$ and testing $N=41$: $\frac{11!\cdot30!}{29!\cdot12!}=\frac{30}{12}=\frac52$. So $N=41$ and $n=21$. Answer (3).

Q. Suppose A and B are the coefficients of $30^{\text{th}}$ and $12^{\text{th}}$ terms respectively in the binomial expansion of $(1+x)^{2n-1}$. If $2A=5B$, then $n$ is equal to :

Explanation

Reviewed by Dr. Abubacker

Want to attempt the full paper?