Given the following series:
[tex]27,9,3,1,\frac{1}{3},\frac{1}{9},.....[/tex]The given series is a geometeric sequence
the first term = 27
And the common differnce = 1/3
we will use the following formula to find sum of the series as the number of terms tends to infinite:
[tex]S_{\infty}=\frac{a}{1-r}[/tex]substitute a = 27, and r = 1/3
[tex]S_{\infty}=\frac{27}{1-\frac{1}{3}}=\frac{27}{\frac{2}{3}}=40\frac{1}{2}=40.5[/tex]So, the answer will be, the sum of the infinite series = 40.5
