Question

Can someone show me how one would find if The sum of 1/3^n would converge? I don't know what test to use...

Answer 1

I'm thinking comparison test, but I don't know how to show anything besides p-test

Answer 2

\[\sum_{n=1}^{\inf} 1/3^n\]

Answer 3

Here is what I am thinking:

Answer 4

ohhhh a geometric sequence! so you are saying the geometric series is 3^(-n)? I can use that to compare it to.

Answer 5

The first term would be 1/3, right?

So, a = 1/3

The common ratio, r = also 1/3.

Answer 6

=1/2, satisfying |r|<1, Thanks!

Answer 7

3^(-n) is the same as (1/3)^n

So, I did 1/3 /(1 - (1/3) ) = 1/2 which is what you got.