Originally Posted by

**badBKO** consider the series

(1+1) + (0.3-.4642) + (0.03 + .2154) + (0.003 - .1000) + (.0003 + .0464) + ..........

I found the series to be:

$\displaystyle \Sigma_{n=0}^{\infty} {3(1/10)^n} + (-1)^{n+1}(1/\sqrt[3]{10})^n

$

I found it to be convergent because 3\Sigma_{n=0}^{\infty} (1/10)^n converges by geometric series test because r= |1/10| < 1

and

$\displaystyle

\Sigma_{n=0}^{\infty} (-1)^{n+1} (1/\sqrt[3]{10})^n

$

converges by geometric series test becuse the |r| < 1 also

so...

the series

math]

\Sigma_{n=0}^{\infty} {3(1/10)^n} + (-1)^{n+1}(1/\sqrt[3]{10})^n

[/tex]

would convergem but then I have to find the EXACT sum of the series and I don't know how to do this.