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The total number of terms which are depe...

The total number of terms which are dependent on the value of `x` in the expansion of `(x^2-2+1/(x^2))^n` is equal to `2n+1` b. `2n` c. `n` d. `n+1`

A

` 2n+1`

B

2n

C

` n+ 1`

D

n

Text Solution

Verified by Experts

The correct Answer is:
b
Now , ` (x^(2) - 2+ (1)/(x^(2)))^(n) = (x^(4) - 2x^(2) + 1)^(n))/(x^(2n)) = ((x^(2) - 1)^(2n))/(x^(2n))`
` therefore ` Total number of terms that are depandent of x is equal to
number of terms in the expansin of ` (x^(2) -1)^(2n)` that have
degree of x different from 2n , which is given by
` (2n+1) - 1= 2pi` .
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