Hi, I\'m stuck on how the series in step one is identified as1/1-x This is the s

Question

Hi, I'm stuck on how the series in step one is identified as1/1-x

This is the step that says we recognize that the expression is:

1+x+x^2+x^3....1/(1-x)

My problem is that I don't recognize that the series can berepresented by the 1/1-x

Where can I find a good list of rules for these formulae?

I'm sort of equally flummoxed by the manipulation at the bottom ofstep three that leads to a similar conclusion that this sequence isrepresented by 1/(1-x)^2

It's as if you have to know the sequence is there ahead of time andyou already must know to look for the patterns and how to identifythe related formula.

Are there simple rules for these, and if so, what's a goodreference? It's been a while since my last math class (hadmath through calculus, but it's been many years).

Explanation / Answer

recognisation of the series can be done by practice onlythere no rules to identify a series. here is the link contans few expansions of theseries http://en.wikibooks.org/wiki/Calculus/Taylor_series i feel if we have all the expansions in our mindwe can identify the required easily ...............this can be doneby every day revisoin of the formulas

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