Question

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

• A. 2n
• B. 3n
• C. 2n+1
• D. 3n+1

Answer 1

The correct option is C 2n+1

Number of terms in expansion of ${(x^2+1+\frac{1}{x^2})}^2$ is

$\therefore$ Lowest power would be $x^{-n}$

$\therefore$ highest power would be $x^n$

Since it has continuous power of $x(-1,0,1)$

Expansion would have powers ranging from $-n$ to n

$\therefore$ Hence there will be $2n+1$ terms.