Find a specific geometric series which sums to 30

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- Nov 27th 2010, 02:47 PMthamathkid1729Geometric Series
Find a specific geometric series which sums to 30

- Nov 27th 2010, 02:55 PMPlato
- Nov 27th 2010, 04:01 PMthamathkid1729
Thank you

Is it possible to find a geometric series summing to -1/3? - Nov 27th 2010, 04:11 PMPlato
A geometric series converges if and only if $\displaystyle |r|<1$.

Apply my first reply. - Nov 27th 2010, 04:24 PMthamathkid1729
So since r = 4, the answer is NO?

- Nov 27th 2010, 04:50 PMskeeter
- Nov 27th 2010, 05:37 PMthamathkid1729
Can only rational numbers be sums of geometric series? Precisely which real numbers can be sums of geometric series?

- Nov 27th 2010, 05:42 PMskeeter
- Nov 28th 2010, 02:24 AMHallsofIvy
The series $\displaystyle \sum_{n=0}^\infty ar^n$ sums to $\displaystyle \frac{a}{1- r}$. Whether that is a rational number or an irrational number depends upon a and r. For example, given any rational number, u, take a= 1 and solve $\displaystyle \frac{1}{1- r}= u$. Given any irrational number, v, take a= v/2 and a= 1/2.