Question

Calculate the sum of the infinite series

Answer 1

ANSWER

$S_ \infty = \frac{40}{3}$

EXPLANATION

The given series is

$20-10+5-...$


The first term of the series is,

$a_1=20$

The common ratio of this series is,

$r = \frac{ - 10}{20}$

This simplifies to,

$r = - \frac{1}{2}$

The sum to infinity of this sequence is given by the formula,

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

We substitute the above values into the formula to obtain,

$S_ \infty = \frac{20}{1- - \frac{1}{2} }$

This simplifies to,

$S_ \infty = \frac{20}{1 + \frac{1}{2} }$

We simplify the denominator to get,

$S_ \infty = \frac{20}{ \frac{3}{2} }$

This will finally give us,

$S_ \infty =20 \times \frac{2}{3}$

$S_ \infty = \frac{40}{3}$

The correct answer is A.

Answer 2

Answer:

A. 40/3  is the correct choice