Represent (1+x)/(1-x) as a power series.
The Attempt at a Solution
I started with 1/ (1-x) = sum (x)^n n= 0 - infinity
(1 + x) sum x^n
and this is where I am stuck.
You got that the power series is 1+2x+2x^2+2x^3+..., I hope? Writing out terms never hurts. And if you've just started on the subject, I'd say you should always do it until it becomes clearer. No, no shortcut really except for adjusting indices between series with different starting points.ohh i see it now, thanks you. My class just started this section and I'm kinda new to this. Is there a shortcut of doing this or I have to write out the terms to find power series?
No, if you use the technique I suggested, you get a first term of +1, not -1. Dick's approach and mine yield the same results.I'm very thankful for this tread, as I ran into the same problem as cheater1.
I would like to point out, however, that while with Dick's method the 1st term of the series is 1, with Mark44's the first term appears to be -1. Any help in understanding why this is so would be greatly appreciated.
If you could tell me how I may be doing this wrongly, I'd really appreciate it ..You are doing the division incorrection. When you divide 1 + x by 1 - x, the first term you get is 1, not -1.