Calculate the sum of the infinite series

Question

asked Dec 24, 2019 121k views

1 Answer

Irakli · Answer 1 · 2019-12-31T04:27:35+0000

Answer:

$S_\infty=250$ .

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.