What is the sum of an infinite geometric series 2=5and r=1/3

The sum to infinite = 7.5

Step-by-step explanation:

Lets revise the geometric sequence

- There is a constant ratio between each two consecutive numbers

Ex:

5  ,  10  ,  20  ,  40  ,  80  ,  ………………………. (×2)

5000  ,  1000  ,  200  ,  40  ,  …………………………(÷5)

* General term (nth term) of a Geometric Progression:

∵ U1 = a  ,  U2  = ar  ,  U3  = ar2  ,  U4 = ar3  ,  U5 = ar4

∴ Un = a(r^n-1), where a is the first term , r is the constant ratio

  between each two consecutive terms  and n is the position

  of the term in the sequence

* The sum of first n terms of a Geometric Progression is calculate

  from Sn = [a(1 - r^n)]/(1 - r)

* The sum to infinity of a Geometric Progression is:

 S∞ = a/(1 - r), where -1 < r < 1

* In the problem a = 5 and r = 1/3

∵ a = 5 and r = 1/3

∵ S∞ = a/(1 - r)

∴ S∞ = 5/(1 - 1/3) = 5/(2/3) = 15/2 = 7.5

77

step-by-step explanation:

step-by-step explanation: