Thread: [SOLVED] sum of series

I am supposed to tell whether this converges or diverges and if it converges tell what it converges to. I'm unclear on how to do the last part.

the summation from n=0 to infinity of 3^(n+1)/4^(n-2)

I used the ratio test and found that it converges. I don't know what to do now.

It is equal to .

Originally Posted by maddas

It is equal to .

what?

I don't know anything about this. And no matter how many different ways I ask this I just get answers that are too complicated for me to understand. I have to figure this out by 9 am. And I don't have a clue as to what I'm doing.

Well, write it all out.



Now factor the later part like



The sum in parenthesis is geometric. You should know that 1+r+r^2+...=1/(1-r) for |r|<1. So in this case



Now what does this expression equal?

Get it? You probably shouldn't wait until the morning before to figure this stuff out :/

Originally Posted by maddas

Well, write it all out.



Now factor the later part like



The sum in parenthesis is geometric. You should know that 1+r+r^2+...=1/(1-r) for |r|<1. So in this case



Now what does this expression equal?

Get it? You probably shouldn't wait until the morning before to figure this stuff out :/

I just got the assignment Fri and I've been trying to figure this out all weekend. And it sorta makes sense. I've never learned about geometric sequences.