Question

How do you find the sum of the infinite geometric series 2+2/3+2/9+2/27+...?

Answer 1

`3.`

Explanation:

Let `s` denote the reqd. sum. Then, we know that,

`s=a/(1-r)`, where, `a=` the first term of the series, and, `r,`common ratio, with `|r|<1`.

Here, `a=2`, and `r=`second term/first term`=(2/3)/2=1/3`, hence `|r|<1.`

Therefore, `s=2/(1-1/3)=2/(2/3)=3`