Question

Calculate the sum of the infinite series

Answer 1

`S_\infty=250`.

Explanation:

The given infinite series is
`50+40+32+(128)/(5)+...`.

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

The common ratio is
`r=(40)/(50)`.

`\Rightarrow r=(4)/(5)`.

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

`S_\infty=(a_1)/(1-r)`

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

`S_\infty=(50)/(1-(4)/(5))`

This implies that,

`S_\infty=(50)/((1)/(5))`

This simplifies to,

`S_\infty=50* 5`

`S_\infty=250`.

The correct answer is C.