Math Is Fun Forum

zaitsev

Member

Registered: 2006-10-12

Posts: 2

[Problem] Summation of a sequence

Hi all,
I need help with a "proving" math question and here it is:

working it out, I get:

the summation of 2^(r+1) - 2^r  is workable, but I have no idea on the summation of r2^r part.
Maybe there is another better way to it? or the method of differences ( f(n) - f(0) ) should be applied here?
Any help would be much appreciated!

Last edited by zaitsev (2006-10-12 23:35:58)

Dross

Member

Registered: 2006-08-24

Posts: 325

Re: [Problem] Summation of a sequence

Have you tried induction?

Let your statement be P(n). Then P(1) is true (try this and see).

Now assume P(k) is true, and try and prove that P(k+1) is true:

So the truth of P(k) implies the truth of P(k+1), axiom of induction etc.

QED

Last edited by Dross (2006-10-13 01:23:17)

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zaitsev

Member

Registered: 2006-10-12

Posts: 2

Re: [Problem] Summation of a sequence

Thanks, Dross!
The only problem now is that I have to show the solution to a group of classmates who have no idea at all on induction.
but oh well, I've learned something new here.
Any other ways of solving it would be appreciated too!