I'm stuck on what I should do for this problem:
Show that the series
\(\displaystyle 1-\frac{2}{5^2}+\frac{3}{5^3}-\frac{4}{5^4}+\cdot \cdot \cdot\) is convergent.
I'm fairly sure that this is an alternating series because the 2nd part of the problems asks to find an estimate with an error less than \(\displaystyle \frac{1}{10,000}\). So, I tried to come up with a formula for the sequence b[sub:1r0jc46r]n[/sub:1r0jc46r] to show it fulfills the conditions of an alternating series, but I couldn't seem to find a formula that could include that first term.
Am I going about this the wrong way? This seems like it should be a straight-forward problem... :?
Any help would be appreciated!
Show that the series
\(\displaystyle 1-\frac{2}{5^2}+\frac{3}{5^3}-\frac{4}{5^4}+\cdot \cdot \cdot\) is convergent.
I'm fairly sure that this is an alternating series because the 2nd part of the problems asks to find an estimate with an error less than \(\displaystyle \frac{1}{10,000}\). So, I tried to come up with a formula for the sequence b[sub:1r0jc46r]n[/sub:1r0jc46r] to show it fulfills the conditions of an alternating series, but I couldn't seem to find a formula that could include that first term.
Am I going about this the wrong way? This seems like it should be a straight-forward problem... :?
Any help would be appreciated!