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

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

Binomial Theorem

Solution:

$\left(\left(x+\frac{1}{x}\right)^2-1\right)^n={ }^n C_0\left(x+\frac{1}{x}\right)^{2 n}-{ }^n C_1\left(x+\frac{1}{x}\right)^{2 n-2}+\ldots .+{ }^n C_n(-1)^n$
Total number of terms $=2 n+1$