Question

27,9,3,1,1/3,1/9......Find the sum of the infinite series. ________________

Answer 1

Given the following series:

$27,9,3,1,\frac{1}{3},\frac{1}{9},.....$

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:

$S_{\infty}=\frac{a}{1-r}$

substitute a = 27, and r = 1/3

$S_{\infty}=\frac{27}{1-\frac{1}{3}}=\frac{27}{\frac{2}{3}}=40\frac{1}{2}=40.5$

So, the answer will be, the sum of the infinite series = 40.5