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#1 2009-09-24 08:51:58

bossk171
Member
Registered: 2007-07-16
Posts: 305

infinite series

Can someone please help me show that:

Partial sums in Excel imply it, and Wolfram Alpha confirms it, but how do you go about proving it?


There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

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#2 2009-09-24 09:20:37

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: infinite series

This is one of those arithmetic–geometric hybrid series.

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#3 2009-09-24 09:33:15

bossk171
Member
Registered: 2007-07-16
Posts: 305

Re: infinite series

That's a pretty cool solution, thanks.

Is this a method you just knew because you had seen it before, or did you come to this after being inspired?

I'm just curious, thanks.


There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

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#4 2009-09-24 09:59:48

Avon
Member
Registered: 2007-06-28
Posts: 80

Re: infinite series

Since you can differentiate a power series term by term within the radius of convergence the following are all valid when |x| < 1

and your result follows with x = 1/2

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