Question

The coefficient of 1/x in the expansion of (1+x)ⁿ (1+1/x)ⁿ is :

A. \(\frac{n!}{\{(n-1)!(n+1)!\}}\)

B. \(\frac{(2n!)}{[(n-1)!(n+1)!]}\)

C. \(\frac{(2n!)}{[(2n-1)!(2n+1)!]}\)

D. None of these

Answer 1

Option : (B)

(1+x)ⁿ (1+1/x)ⁿ

For x^-1;

⇒ k-n = -1 

⇒ k = n-1 

So, coefficient = \(\frac{2n!}{(n-1)!(n+1)!}\)