Find the coefficient of `x^n` in the expansion of `(1-9x+20 x^2)^(-1)dot`
Find the coefficient of `x^n` in the expansion of `(1-9x+20 x^2)^(-1)dot`
5 views
1 Answers
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)`.
5 views
Answered