First slide

Binomial theorem for positive integral Index

Question

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

Moderate

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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