Question

Calculate the sum of the infinite series

Answer 1

A. 40/3 is the correct choice

Answer 2

ANSWER


`S_ \infty = (40)/(3)`

Step-by-step 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 = ( - 10)/(20)`

This simplifies to,


`r = - (1)/(2)`

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


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

We substitute the above values into the formula to obtain,


`S_ \infty = (20)/(1- - (1)/(2) )`

This simplifies to,


`S_ \infty = (20)/(1 + (1)/(2) )`

We simplify the denominator to get,


`S_ \infty = (20)/( (3)/(2) )`

This will finally give us,


`S_ \infty =20 * (2)/(3)`


`S_ \infty = (40)/(3)`

The correct answer is A.