My Math Forum Series Computation.

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 November 14th, 2010, 10:49 AM #1 Math Team   Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,990 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus Series Computation. [color=#000000]Compute the series $\bf\sum_{k=0}^{+\infty}\frac{(-1)^{n}(2n+1)}{2n^2+2n+1}$[/color].
 November 14th, 2010, 05:04 PM #2 Senior Member     Joined: Oct 2010 From: Changchun, China Posts: 492 Thanks: 14 Re: Series Computation. $\text{sech}(z)=\pi\sum_{n=0}^{\infty}\frac{(-1)^{n}(2n+1)}{\pi^2(n+\frac{1}{2})^2+z^2}$ $\text{sech}(\frac{\pi}{2})=\pi\sum_{n=0}^{\infty}\ frac{(-1)^{n}(2n+1)}{\pi^2(n+\frac{1}{2})^2+(\frac{\pi}{2 })^2}=\frac{2}{\pi}\sum_{n=0}^{\infty}\frac{(-1)^{n}(2n+1)}{2n^2+2n+1}$ $\sum_{n=0}^{\infty}\frac{(-1)^{n}(2n+1)}{2n^2+2n+1}=\frac{\pi}{2}\text{sech}( \frac{\pi}{2})=\frac{\pi}{e^{\frac{\pi}{2}}+e^{-\frac{\pi}{2}}}$
 November 15th, 2010, 12:57 AM #3 Math Team   Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,990 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus Re: Series Computation. [color=#000000]Suppose we didn't know the above, can you think of a complex technique?[/color]
November 15th, 2010, 06:54 AM   #4
Senior Member

Joined: Oct 2010
From: Changchun, China

Posts: 492
Thanks: 14

Re: Series Computation.

Quote:
 Originally Posted by ZardoZ [color=#000000]Suppose we didn't know the above, can you think of a complex technique?[/color]
Sorry, I really dunno what to do. show me please

 November 15th, 2010, 12:47 PM #5 Math Team   Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,990 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus Re: Series Computation. [color=#000000]Why do you have to be sorry? We are scientists , seek and you shall find, ask and you shall receive! I cannot understand why pdf uploading is not allowed , if it is something big without the ability to edit it after an hour, discourages people from uploading big answers. Anyway see here.[/color]
 November 15th, 2010, 03:57 PM #6 Senior Member     Joined: Oct 2010 From: Changchun, China Posts: 492 Thanks: 14 Re: Series Computation. Sorry, I cannot see this document, cuz the Chinese government put a big firewall on the door outside, so we cannot visit many websites, such as Wiki . I just wonder if you'd mind sending me an e-mail about this.... my address: stainburg@gmail.com. Thanks a lot. By the way, sometimes, I use screen shot software to convert a document to pics, and then, we can upload pics here.
November 15th, 2010, 04:13 PM   #7
Math Team

Joined: Nov 2010
From: Greece, Thessaloniki

Posts: 1,990
Thanks: 133

Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus
Re: Series Computation.

[color=#000000]In case someone else has problems too.[/color]
Attached Images
 On Series Probelm.gif (20.4 KB, 479 views)

 November 15th, 2010, 04:16 PM #8 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Series Computation. I was just about to post a pic of your pdf because I thought you were asleep!
 November 15th, 2010, 04:18 PM #9 Math Team   Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,990 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus Re: Series Computation. [color=#000000]When you drink too much coffee , this is what happens.[/color]
 November 15th, 2010, 04:22 PM #10 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Series Computation. I understand the coffee in Greece is strong by American standards!

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