Finding the sum of the infinite series Hi I am trying to solve the sum of the series of this problem:
$$
11 + 2 + \frac 4 {11} + \frac 8 {121} + \cdots
$$
I know its a geometric series, but I cannot find the pattern around this. 

Your series is a geometric series with a common ration of $q =\dfrac{2}{11}$ and a first term $a_0$ equal to $11$.
$-1 < \dfrac{2}{11}< 1$ so the series is convergent.
Its sum is equal to
$$a_0 \cdot \dfrac{1}{1-q} = 11 \cdot \dfrac{1}{1-\dfrac{2}{11}} = \dfrac{121}{9}$$
