Math Is Fun Forum

bossk171

Member

Registered: 2007-07-16

Posts: 305

Infinite series

Can anyone provide me with a proof of

I have one, but it's long and very roundabout. Can anyone show a to-the-point proof?

Last edited by bossk171 (2007-09-17 05:15:50)

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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.

HallsofIvy

Guest

Re: Infinite series

Can anyone provide me with a proof of

I have one, but it's long and very roundabout. Can anyone show a to-the-point proof?

One way to do that is to note that this is

  Of course each term of term of the sum in parentheses is the derivative of

. That is, it is the derivative of the sum

.  And THAT is a part of a geometric series with r= x:

is a geometric series having sum, by the standard formula,

.  The reason it is only "part" is that it is missing the first "1".  So

and so the original sum, multiplying by x, is

.

  Is your proof longer and more roundabout than that?

bossk171

Member

Registered: 2007-07-16

Posts: 305

Re: Infinite series

A little bit, they're very similar. but yours is better. Thankyou.

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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.

mamoo

Member

Registered: 2007-09-06

Posts: 3

Re: Infinite series

but y u didn't start with

and use binomial expansion?
would not it be better?

Last edited by mamoo (2007-09-17 09:28:00)