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  • Find the coefficient of x ^1/17 in the expansion of (x^4-1/x^3) ^15

Find the coefficient of x1/17 in the expansion of (x4 – 1/x3)15

 

Answers (1)

Given: (x4 – 1/x3)15

Thus,

Tr+1 = 15Cr(x4)15-r(-1/x3)r

                 = 15Cr x60-4r(-1)r x-3r

                 = 15Cr x60-7r(-1)r

Now, for coefficient x-17,

60 – 7r = -17

7r = 77

r = 11

Thus, T11+1 = 15C11 x60-77(-1)11

Therefore,

Coefficient of x-17 = -15 x 14 x 13 x 12 x 11!/11! x 4 x 3 x 2 x 1

                              = -1365
 

Posted by

infoexpert22

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