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Find the coefficient of x^n in the expan...

Find the coefficient of `x^n` in the expansion of `(1-9x+20 x^2)^(-1)dot`

Text Solution

Verified by Experts

We have ,
`(1-px+20x^(2))^(-1)=[(1-5x)(1-4x)]^(-1)`
`= (1)/((1-5x)(1-4x)) = (5)/(1-5x) - (4)/(1-4x)`
` = 5 (1-5x)^(-1)-4(1-4x)^(-1)`
`= 5[1+5x+(5x)^(2)+"....."+(5x)^(n)+"...."]-4[1+4x+(4x)^(2)+"...."+(4x)^(n)+"...."]`
Therefore, the coefficient of `x^(n)` is `5^(n+1)-4^(n+1)`.
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