1. ## Geometric Series

Find a specific geometric series which sums to 30

2. Originally Posted by thamathkid1729
Find a specific geometric series which sums to 30
Can you solve $\displaystyle \dfrac{1}{1-r}=30~?$

3. Thank you
Is it possible to find a geometric series summing to -1/3?

4. A geometric series converges if and only if $\displaystyle |r|<1$.

5. So since r = 4, the answer is NO?

6. Originally Posted by thamathkid1729
Thank you
Is it possible to find a geometric series summing to -1/3?
$\displaystyle \displaystyle -\left(\frac{1}{4} + \frac{1}{4^2} + \frac{1}{4^3} + ... \right) = -\frac{1}{3}$

7. Can only rational numbers be sums of geometric series? Precisely which real numbers can be sums of geometric series?

8. Originally Posted by thamathkid1729
Can only rational numbers be sums of geometric series? Precisely which real numbers can be sums of geometric series?
the sum can be any real number ... depends on the first term and the common ratio.

9. 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.