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Question

Find the 13th term in the expansion of (9x13x)18,x0

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Solution

It is known that(r+1) term (Tr+1) in the binomial expansion of (a+b)n is given by Tr+1=nCranrbr
Thus 13th term in the expansion of (9x13x)18 is
T13=T12+1=18C12(9x)1812(13x)12
=(1)1218!12!6!(9)6(x)6(13)12(1x)12
=18.17.16.15.14.13.12!12!.6.5.4.3.2.x6(1x6).312(1312)
=18564

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