ধারা

The total number of terms which are dependent on the value of xx in the expansion of (x2−2+1x2)n\left(x^2 - 2 + \displaystyle\frac{1}{x^2}\right)^n is equal to   

কাজু বাদাম

(x2−2+1x2)n(x^2-2+\dfrac{1}{x^2})^{n}

=((x−1x)2)n=((x-\dfrac{1}{x})^2)^{n}

=(x−1x)2n=(x-\dfrac{1}{x})^{2n}

Tr+1= 10Crx2n−2rT_{r+1}=\:{10}C_{r}x^{2n-2r}

For term independent of xx

2n−2r=02n-2r=0

n=rn=r

Hence there will be 11 term independent of xx.

Since the total number of terms are 2n+12n+1.

Hence the total number of term dependent on xx will be

Total number of terms-(total number of terms independent of xx).

=2n+1−1=2n+1-1

=2n=2n

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