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Find the coefficient of x^(18) in (x^2+2...

Find the coefficient of `x^(18)` in `(x^2+2+1/(x^2))^(-5)(1+x^2)^(40)dot`

Text Solution

Verified by Experts

Given expansion is
`E = ((x+(1)/(x))^(2))^(-5) (1+x^(2))^(40)`
`= ((x^(2) + 1)/(x))^(-10) (1+x^(2))^(40) = x^(10)(1+x^(2))^(30)`
Coefficient of `x^(20)` in E = Coefficient of `x^(10)` in `(1+x^(2))^(30)`
`= .^(30)C_(5)`
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