Answer
The Sum of the given infinite geometric series = 6
Work Step by Step
The Sum of a infinite geometric series ( if | r | $\lt$ 1 ) is given by
S = $\frac{First term }{1 - common ratio}$ = $\frac{a_{1}}{1 - r}$
The given infinite geometric series
= 5 + $\frac{5}{6}$ + $\frac{5}{6^{2}}$ + $\frac{5}{6^{3}}$ + ......................
= 5 + $\frac{5}{6}$ + $\frac{5}{36}$ + $\frac{5}{216}$ + ......................
Here
First term $a_{1}$ = 5
common ratio r = $\frac{\frac{5}{216}}{\frac{5}{36}}$ = $\frac{\frac{5}{36}}{\frac{5}{6}}$ = $\frac{\frac{5}{6}}{5}$ = $\frac{1}{6}$
The Sum of the given infinite geometric series = $\frac{a_{1}}{1 - r}$ = $\frac{5}{1 - \frac{1}{6}}$ = $\frac{5}{\frac{5}{6}}$ = 5$\times$$\frac{6}{5}$ = 6
