# Thread: Determine whether the infinite geometric series converges or diverges.

2. ## Re: Determine whether the infinite geometric series converges or diverges.

common ratio is greater than 0 and less than 1 ... what does that tell you?

3. ## Re: Determine whether the infinite geometric series converges or diverges.

Originally Posted by rehaddeed197
Here is the basic idea: $\left( {\forall \left| r \right| < 1} \right)\left[ {\sum\limits_{k = 0}^\infty {a{r^k}} = \frac{a}{{1 - r}}} \right]$

Notice that $\sum\limits_{k = 1}^\infty {4{{\left[ {\frac{1}{3}} \right]}^{k - 1}}} = \sum\limits_{k = 0}^\infty {\frac{4}{{{3^k}}}}$

4. ## Re: Determine whether the infinite geometric series converges or diverges.

Reheddaad, what do you know about geometric series? The answer to this question follows from some pretty basic facts about geometric series.