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Question

Show that the expansion of (x2+1x)12 does not contian any term involving x1.

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Solution

Any term in the expansion of (x2+1x)12 is

TN=Tr+1=nCrxnryr

=12Cr(x2)12r(1x)12

=12Crx242rx12

=x122r=x1

12-2r=-1

2r=13

r=132

r can not be a fraction, therefore there is no term in the expansion of (x2+1x)12having the term x1.


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