Question

Find the $(n+1{)}^{th}$ term from the end in the expansion of ${(x-\frac{1}{x})}^{2n}$

• A. ${(-1)}^n.{{}^{2n}C}_n$
• B. ${(-1)}^{n+1}.{{}^{2n}C}_{n-1}$
• C. ${(-1)}^n.{{}^{2n}C}_{n-1}$
• D. None of these

Answer 1

Answer: (A)

${(-1)}^n.{{}^{2n}C}_n$

There are total $2n+1$ terms in the given expansion.

Hence $(n+1{)}^{th}$ term, from the end is the $(n+1{)}^{th}$ term form beginning the beginning also since, it is the middle term.

$T_{n+1}$$={}^{2n}{C}_n{x}^n(-\frac{1}{x^n}{)}^n$

$=(-1{)}^n{}^{2n}{C}_n$