Math Is Fun Forum

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?

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

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: infinite series

This is one of those arithmetic–geometric hybrid series.

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.

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

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