# Geometric Series

• Nov 27th 2010, 03:47 PM
thamathkid1729
Geometric Series
Find a specific geometric series which sums to 30
• Nov 27th 2010, 03:55 PM
Plato
Quote:

Originally Posted by thamathkid1729
Find a specific geometric series which sums to 30

Can you solve $\dfrac{1}{1-r}=30~?$
• Nov 27th 2010, 05:01 PM
thamathkid1729
Thank you
Is it possible to find a geometric series summing to -1/3?
• Nov 27th 2010, 05:11 PM
Plato
A geometric series converges if and only if $|r|<1$.
• Nov 27th 2010, 05:24 PM
thamathkid1729
So since r = 4, the answer is NO?
• Nov 27th 2010, 05:50 PM
skeeter
Quote:

Originally Posted by thamathkid1729
Thank you
Is it possible to find a geometric series summing to -1/3?

$\displaystyle -\left(\frac{1}{4} + \frac{1}{4^2} + \frac{1}{4^3} + ... \right) = -\frac{1}{3}$
• Nov 27th 2010, 06:37 PM
thamathkid1729
Can only rational numbers be sums of geometric series? Precisely which real numbers can be sums of geometric series?
• Nov 27th 2010, 06:42 PM
skeeter
Quote:

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.
• Nov 28th 2010, 03:24 AM
HallsofIvy
The series $\sum_{n=0}^\infty ar^n$ sums to $\frac{a}{1- r}$. 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 $\frac{1}{1- r}= u$. Given any irrational number, v, take a= v/2 and a= 1/2.