Hi, I'm stuck at proving the following question...

Prove that for all n>0,

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

I've tried all sorts of different ways of solving this, but to no avail.

Any help is appreciated :)

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- Jan 19th 2010, 08:26 PMseven.jHelp with a proof.
Hi, I'm stuck at proving the following question...

Prove that for all n>0,

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

I've tried all sorts of different ways of solving this, but to no avail.

Any help is appreciated :) - Jan 19th 2010, 08:50 PMDrexel28
- Jan 19th 2010, 08:54 PMKrizalid
you can do the rest, those are finite geometric sums.

- Jan 19th 2010, 09:37 PMSoroban
Hello, seven!

Here's one way . . .

Quote:

Prove that for all

. .

. . . .[1]

The geometric series has the sum: .

Then [1] becomes: .

Multiply by 2: .

- Jan 19th 2010, 10:19 PMJhevon