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Question
Find the coefficient of x15 in `(x^2 + 1/x^3)^10`
Solution
General term Tr+1 = `""^10"C"_"r" (x^2)^(10-"r") (1/x^3)^"r"`
= `""^10"C"_"r" x^(20-2"r") 1/(x^3"r")`
= `""^10"C"_"r" x^(20 - 2"r")* x^(-3"r")`
= `""^10"C"_"r" x^(20 - 5"r")`
To find coefficient of x15 we have to equate x power to 15
i.e. 20 – 5r = 15
20 – 15 = 5r
⇒ 5r = 5
⇒ r = `5/5` = 1
So the coefficient of x15 is 10C1 = 10
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