Calculate the sum of the infinite series S(infinity)=20-10+5-...

Question

asked Mar 11, 2019 182k views

2 Answers

Mehdi Faraji · Answer 1 · 2019-03-17T12:28:53+0000

Answer:

$S(\infty)=(40)/(3)$

Explanation:

we are given series as

S(infinity)=20-10+5-..

Firstly, we will check type of series

first term=20

second term=-10

third term =5

now, we can find common ratios

r=(-10)/(20) =-0.5

r=(5)/(-10) =-0.5

we can see that both ratios are equal

so, this is geometric series

we can use sum of infinite terms formula

$S(\infty)=(a)/(1-r)$

where a is first term

a=20

r=-0.5

now, we can plug values

$S(\infty)=(20)/(1+0.5)$

$S(\infty)=(40)/(3)$