Geometric Series

**thamathkid1729** · November 27th 2010, 02:47 PM

Find a specific geometric series which sums to 30

**Plato** · November 27th 2010, 02:55 PM

Originally Posted by thamathkid1729

Find a specific geometric series which sums to 30

Can you solve $\dfrac{1}{1-r}=30~?$

**thamathkid1729** · November 27th 2010, 04:01 PM

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

**Plato** · November 27th 2010, 04:11 PM

A geometric series converges if and only if $|r|<1$ .
Apply my first reply.

**thamathkid1729** · November 27th 2010, 04:24 PM

So since r = 4, the answer is NO?

**skeeter** · November 27th 2010, 04:50 PM

Originally Posted by thamathkid1729

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

$\displaystyle -\left(\frac{1}{4} + \frac{1}{4^2} + \frac{1}{4^3} + ... \right) = -\frac{1}{3}$

**thamathkid1729** · November 27th 2010, 05:37 PM

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

**skeeter** · November 27th 2010, 05:42 PM

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.

**HallsofIvy** · November 28th 2010, 02:24 AM

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.

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