Math Is Fun Forum

wednesday

Member

Registered: 2010-09-18

Posts: 7

Mathematical Induction

Hi, I could use some help with this ...

1/2+3/2²+...+(2n-1)/2^n=1+2(1-1/(2^(n-1))-(2n-1)/2^n

Last edited by wednesday (2010-10-09 04:36:03)

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bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mathematical Induction

Hi wednesday;

Is your problem stated like this?

What are you trying to do? Prove it by induction?
Or use the summation calculus as someone already has, to get the RHS?

I will try by induction first:

The base step when n = 1, 1/2 = 1/2 , okay.

To shorten the algebra I am going to use a little notational trickery on the right hand side.

If that is true and the next is true we will have a proof by induction. The next is

we can replace most of the LHS by 1).

Can you finish from here? It is all algebra but you will find RHS = LHS.

So proved by induction.

You know summing the series by direct methods such as the summation calculus and the Euler Mclaurin summation formula would be a proof and probably easier.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
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