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In the expansion of (x^(2) + 1 + (1)/(x^...

In the expansion of `(x^(2) + 1 + (1)/(x^(2)))^(n), n in N`,

A

2n

B

3n

C

`2n+1`

D

`3n +1`

Text Solution

Verified by Experts

The correct Answer is:
c
We have, lttbrgt `(x^(3)+ 1 + (1)/(x^(3)))^(n) = (1)/(x^(3n) )(1 + x^(3) + x^(6))^(n) = (1)/(t^(n))(1 + t + t^(2))^(n)`, where ` t x^(3)`
Clearly, `(1 + t + t^(2))^(n)` , when expanded, is a polynomial of
degree 2n
Hence, these are (2n +1)` terms .
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