If there is a term independent of x in `( x+1/x^2)^n` , show that it is equal to `(n!)/((n/3)! ((2n)/3)! ) `

Find the term independent of x in (x+1/x)^(2n)

The term independent of x in (1+x)^m (1+1/x)^n is

The term independent of x in (1+x)^m (1+1/x)^n is

Find the term independent of x in (1+3x)^(n)(1+(1)/(3x))^(n) .

The term independent of x in (1+x+x^(-2)+x^(-3))^(10) is n then the last digit of (n+2)^(n) is

The term independent of x in the expansion of (1 + x)^n (1 + 1/x)^n is

If the 5th term is the term independent of x in the expansion of (x^(2//3) + 1/x)^n then n =

Let P_n=((1+x)(1-x^2)(1+x^3)(1-x^4))/({(1+x)(1-x^2)(1+x^3)(1-x^4)(1-x^(2n))}^2) .Let the term independent of x in the expansion of (x^2+1/x^2+2)^(2n) is equal to lim_(x->-1) Pn . then

Prove that the term independent of x in the expansion of (x+1/x)^(2n) \ is \ (1. 3. 5 ... (2n-1))/(n !). 2^n .

If a term independent of x is to exist in the expansion of (x + (1)/(x^2))^n then n must be