Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Possible Duplicate:
Value of $\sum\limits_n x^n$

Ive been studying Geometric series and Arithmetic series all day and have struggled to attempt these problems. The Question is to sum up these problems.

1) \begin{align}&\sum_{n=0}^\infty 3^{-n}\end{align} 2) \begin{align}&\sum_{n=2}^\infty 3^{-n}\end{align} 3) \begin{align}&\sum_{n=0}^{n+1} 6^{n}\end{align}

Is it correct to say they are not geometric series because for 1) r=3 so r>1? So what formula do I use on these problems? I'm struggling to find the formulas to use.

Thanks. Apologies if I have asked this question the wrong way.

share|cite|improve this question

marked as duplicate by Aryabhata, t.b., J. M., Zev Chonoles Apr 29 '12 at 8:52

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

Since $3^{-n} = (\frac{1}{3})^n$, numbers 1 and 2 will converge. Number 3 is also finite, since you are summing only finitely-many terms. – Austin Mohr Apr 6 '12 at 17:40

You overlooked the minus sign in the exponent. Your $r$ in 1) is $\frac{1}{3}$. See if you can do it now, otherwise ping me with a comment and I'll post some more help.

share|cite|improve this answer
Oh dear. I cant believe it. I'm devastated at that mistake. Thank you so much, I lost 4 hours researching this problem. – Shane Apr 6 '12 at 17:45
@Shane pats on Shane's shoulder I know what it feels like. : ) – Rudy the Reindeer Apr 6 '12 at 17:49

A geometric series is defined by the fact that successive terms are in the same ratio, so all the series you are summing are geometric. Whether the sum converges or not, the series can still be geometric. $\begin{align}&\sum_{n=0}^\infty 3^{n}\end{align}$ is still an attempt to sum a geometric series, but the sum is not convergent in this case.

share|cite|improve this answer

Not the answer you're looking for? Browse other questions tagged or ask your own question.