Find partial fraction of $ \dfrac{m^n}{(a^n-b^n)(a^{n+1}-b^{n+1})}$ where m = a $\times b$
$ \dfrac{m^n}{(a^n-b^n)(a^{n+1}-b^{n+1})}$ where m = a $\times b$
We can write it for partial fraction :
$\dfrac{X}{(a^n-b^n)} + \dfrac{Y}{a^{n+1}-b^{n+1}}$
$= X.a^{n+1} -Xa^{n+1} + Y.a^n - b^n Y$
= $a^m(X +3Y) -b^n(X +2Y)$
$\Rightarrow X +3Y =1 $ & $X+2Y =-1$
$\Rightarrow Y =2 $ and $X =-5$ is it right of doing such problems in this manner please suggest and guide.. thanks..