The number of terms in the expansion of (x2+1+(1/x2))n, n ∈ N, is :

Question

The number of terms in the expansion of (x2+1+(1/x2))n, n ∈ N, is : (A) 2 n (B) 3 n (C) 2 n+1 (D) 3 n+1

Tardigrade Admin · Accepted Answer

((x+(1/x))2-1)n= n C0(x+(1/x))2 n- n C1(x+(1/x))2 n-2+ ldots .+ n Cn(-1)n Total number of terms =2 n+1

Q. The number of terms in the expansion of $(x^{2} + 1 + \frac{1}{x ^{2}})^{n}, n \in N$ , is :