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  • Find the total number of term, that are dependent of x in the expansion of <img alt="\small \left(x^2-2+\frac{1}{x^2}\right)^n" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Csmall%20

Find the total number of term, that are dependent of x in the expansion of \small \left(x^2-2+\frac{1}{x^2}\right)^n

Option: 1

n


Option: 2

n+1


Option: 3

n-1


Option: 4

None of these


Answers (1)

best_answer

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

Total number of terms that are dependent on x is equal to number of terms in the expansion of \left(x^2-1\right)^n that have degree of x different from 2n, which is equal to n.
 

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