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The coefficient of x^20 in the expansion...

The coefficient of `x^20` in the expansion of `(1+x^2)^40.(x^2+2+1/x^2)^-5` is:

Text Solution

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`(1+x^2)^40(x^2+2+1/x^2)^(-5)`
`=(1+x^2)^40[(x+1/x)^2]^-5`
`=(1+x^2)^40[((x^2+1)/x)^2]^-5`
`=(1+x^2)^30[1/x^2]^-5`
`=(1+x^2)^30x^10`
`=x^10(C(30,0)*1+C(30,1)x^2+C(30,2)x^4+C(30,3)x^6+C(30,4)x^8+C(30,5)x^10+...C(30,30)x^60)`
So, term with involving `x^20` will be `C(30,5)x^20`.
So, coefficient of `x^20` will be `C(30,5).`
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