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Question

Find the 7th term of (12x)9 when |x|<12

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Solution

(12x)9 is of the form (1+x)n
(1+p)n=nC0(1)n(p)0+nC1(1)n1(p)1+........nCn(1)0(p)1
p=2x
n=9
(12x)9=nC0(1)9(2x)0+9C1(1)8(2x)1+.....
rthterm=nC(r1)(1)(nr+1)(2C)(r1)
7thterm=nC6(1)(96+1)(2x)6
=nC6(2)6x6
7thterm=26nCrx6

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