But I don't know if this is right, or what my nth term would be, much less the power series...Thanks!!

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- April 16th 2009, 08:05 PMmollymcf2009Binomial series #2 stuck!

But I don't know if this is right, or what my nth term would be, much less the power series...Thanks!! - April 16th 2009, 08:15 PMChris L T521
- April 16th 2009, 08:33 PMmollymcf2009
- April 16th 2009, 09:28 PMo_O
Binomial series are given by:

for any and if . Here, and .

So:

_______________

Let's look at the general term:

Just looking at the expanded series, we see that with even , the coefficient is positive and with odd , the coefficient is negative.

So, if we factor out the negative signs:

etc. - April 16th 2009, 09:37 PMmollymcf2009
- April 16th 2009, 10:09 PMo_O
Focus on the expression:

We can simplify it by multiplying by "1":

So you can see why I multiplied both top and bottom by so that I can simplify that long product into a simple factorial.