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Power series

  • Thread starter EV33
  • Start date
  • #1
196
0

Homework Statement



Using the power series for arctan show that pi/4-ln(sqrt(2))=1-1/2-1/3+1/4+1/5...


Homework Equations


arctan=1-(1/3)x^3+(1/5)x^5...(((-1)^n)(x^(2n+1)))/(2n+1)


The Attempt at a Solution



The first thing I noticed was that arctan(1)=pi/4 and represented 1-1/3+1/5...

I am having trouble figuring out what -1/2+1/4-1/6... is equivalent to besides a simple series.

If anyone has any hints. I would love to hear them because I am stuck.
 

Answers and Replies

  • #2
196
0
I have tried converting it back to a geometric series and comparing it to the natural log taylor series but haven't had any luck.
 
  • #3
Char. Limit
Gold Member
1,204
14
What's the sum from n=1 to infinity of [tex]\frac{\left(-1\right)^n}{n}[/tex]? Also, do you see that [tex]log(\sqrt{2}) = \frac{1}{2}log(2)[/tex]?
 
  • #4
196
0
Thank you so much. It is always something simple. That log property makes this problem a lot easier.
 

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