Question

Find the sum of the geometric series.

20-10+5-5/2+ ...

a.
3718/13
b.
40/3
c.
3003/7
d.
715


Please select the best answer from the choices provided

a) A
b) B
c) C
d) D

Answer 1

40/3 option B

Explanation:

20-10+5-5/2+ ...

We need to find the sum of infinite geometric series

`S_n = (a)/(1-r)`

a is the first term (20)

r is the common ratio

To find common ratio we divide second term by first term

r=
`(-10)/(20) = -(1)/(2)`

now we plug in the values

`S_n = (20)/(1-(-(1)/(2))`

`S_n = (20)/(1+(1)/(2))`

`S_n = (20)/((3)/(2))`

`S_n = 20 * (2)/(3)`

sum = 40/3