the sum to infinity

**kasia.ogor** · September 12th 2009, 07:55 AM

For the following geometric serie, find the range of values of x for which the sum to infinity of the serie exist.
$1 + \frac{1}{x} + \frac{1}{x^2} + \frac{1}{x^3} + ...$
Please help me with that problem.

**red_dog** · September 12th 2009, 10:17 AM

Let $S_n=1+\frac{1}{x}+\frac{1}{x^2}+\ldots+\frac{1}{x^ {n-1}}$

Then $S_n=\frac{x}{1-x}\left[\left(\frac{1}{x}\right)^n-1\right]$

$S_n$ converges if $\left|\frac{1}{x}\right|<1\Rightarrow |x|>1\Rightarrow x\in(-\infty,-1)\cup(1,\infty)$

Thread: the sum to infinity

LinkBack

Thread Tools

Display

the sum to infinity

Similar Math Help Forum Discussions

Integral of sech(x) between infinity and minus infinity

If the derivative is bigger than positive constant, is the limit at infinity infinity

Definition of Limit proof: x -> infinity of sqrt(x) - x = -infinity

Limit at infinity equaling infinity?

ilimts w/ result being infinity minus infinity

Search Tags