Question

State the limit of `1/3,1/9,1/27,1/81,1/243....(1/3)^n`?

`1/3,1/9,1/27,1/81,1/243....(1/3)^n`

How do you state the limit of this sequence?

Answer 1

`3/2`

Explanation:

The problem can be rewritten as
`\sum_{n=0}^{oo}(1/3)^n`

And we can see that is a Geometric series. To understand wheather the series converges or not we have to solve the following inequality
`|1/3|<1`

In this case it's easy to say that is alway true
`1/3<1`

So we can finally state that the series converges to the following value
`1/(1-q)` where `q=1/3`

`1/(1-1/3)`

`1/(2/3)`

and the value of convergence is
`3/2`