Question

Calculate the sum of the infinite series

Answer 1

Answer:

$S_\infty=250$.

Step-by-step explanation:

The given infinite series is  $50+40+32+\frac{128}{5}+...$.

The first term of this series is $a_1=50$.

The common ratio is $r=\frac{40}{50}$.

$\Rightarrow r=\frac{4}{5}$.

The sum of this infinite series is given by the formula,

$S_\infty=\frac{a_1}{1-r}$

We now substitute all the above values in to this formula obtain,

$S_\infty=\frac{50}{1-\frac{4}{5}}$

This implies that,

$S_\infty=\frac{50}{\frac{1}{5}}$

This simplifies to,

$S_\infty=50\times 5$

$S_\infty=250$.

The correct answer is C.