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Question

Show that the expansion of x2+1x12 does not contain any term involving x−1.


Solution

Suppose x1 occurs at the (r + 1)th term in the given expression.
Then,
Tr+1=Cr12 (x2)12-r 1xr=Cr12 x24-2r-rFor this term to contain x-1, we must have24-3r=-13r=25r=253It is not possible, as r is not  an integer.

Hence, the expansion of x2+1x12 does not contain any term involving x−1.

Mathematics
RD Sharma XI (2015)
Standard XI

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