Question Number 5752 by Rasheed Soomro last updated on 26/May/16
$$\mathrm{Determine} \\ $$$$\:\:\:\:\mathrm{1}+\frac{{ar}}{{a}+{r}}+\frac{{ar}^{\mathrm{2}} }{{a}+\mathrm{2}{r}}+\frac{{ar}^{\mathrm{3}} }{{a}+\mathrm{3}{r}}+....+\frac{{ar}^{{n}−\mathrm{1}} }{{a}+\left({n}−\mathrm{1}\right){r}} \\ $$