The number of terms whose values depend on x in the expansion of x2−2+1x2n is

The number of terms whose values depend on $x$ in the expansion of ${(x^{2} - 2 + \frac{1}{x^{2}})}^{n}$ is

A
$2 n$
B
$2 n + 1$
C
$2 n - 1$
D
$0$

Solution:

${(x^{2} - 2 + \frac{1}{x^{2}})}^{n} = {(x - \frac{1}{x})}^{2 n}$

Number of terms in the expansion is $(2 n + 1)$ out of

which just one is independent of $x$ .

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