Geometric Series - Finding a Partial Sum Equation

[Sean O]

Is it possible to find the partial sum equation for (2^m - 1)/3^m, from m=0 to m=n-1?

I know that I'm supposed to rearrange the expression into the format ar^m, so the exponent m must only be on the value r, and not on the constant a. So far the farthest I've gotten is to rearrange it into (2/3)^m - (1/3)^m, but I have no idea what to do from there. I'm also not sure how I would go about proving that this expression can't be made into a partial sum, if it turns out it isn't possible.

Any input or hints would be a big help.

 

[yyat]

You can just sum up (2/3)^m and (1/3)^m separately with the usual formula, then subtract the results.

 

[Sean O]

Damn, that's one of those "smack-yourself-for-not-noticing-it" solutions. That makes perfect sense. Thanks for your help.