Expert: Paul Klarreich - 2/2/2009

Question
I have a series X-X^3+X^5-X^7+X^9 etc.. and its starts at K=0 to infinity. I understand theres an addition of 2 in the exponent but, how do I get the switched signs ?


Answer
Questioner:   Nicole
Category:  Advanced Math
Private:  No
 
Subject:  Formula 4 series
Question:  I have a series X-X^3+X^5-X^7+X^9 etc.. and its starts at K=0 to infinity. I understand theres an addition of 2 in the exponent but, how do I get the switched signs ?
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Hi, Nicole,

I am not sure what you are asking.  (What is Formula 4?  I don't even know what Formulas 1,2,3 are.)

Now if you are asking if there is a general expression for the terms of the series,

Yes, there is.

You observed that the exponents increase by 2 to give odd integers each time and the usual expression to produce an odd integer is:

2k + 1,

so you should have  x^(2k + 1) in there.

Now if you want to alternate signs (not switch, alternate) the way to do that is to have (-1) to a power.  If it is an even power, you get +1, odd power gives -1.

Put those together and you'll get your expression.