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Question -

Show that the expansion of (x2 + 1/x)12 does not contain any term involving x-1.



Answer -

Given:

(x2 +1/x)12

If x-1 occursat the (r + 1)th term in the given expression.

Then, we have:

Tr+1 = nCr xn-r ar

For this term tocontain x-1, we must have

24 – 3r = -1

3r = 24 + 1

3r = 25

r = 25/3

It is not possible,since r is not an integer.

Hence, there is noterm with x-1 in the given expansion.

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