Prove that :-

[tex]\displaystyle \sf\sum_{q=1}^{\infty}\left(a^{q}\left(1+\sum_{r=1}^{\infty} \frac{\prod_{i=0}^{r+1}(q-i)}{\Gamma(r+1)}\left(\frac{b x^{m}}{a}\right)^{r}\right)\right)=\frac{a+b x^{m}}{1-\left(a+b x^{m}\right)} [/tex]
if all variables belong to natural number.​