Math Is Fun Forum

harrorm

Member

Registered: 2016-06-27

Posts: 8

Need explanation on a summation transformation

edit: nevermind figured it out!

Last edited by harrorm (2016-07-07 18:06:37)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Need explanation on a summation transformation

Hi;

For one thing expanding out the sum we get:

T(k)->T(1), T(2), T(3)...T(n-2), T(n-1)

T(n-k) -> T(n-1), T(n-2),...T(3), T(2), T(1)

If you do not see that then choose some value for n like 5  and manually do the summation term by term.

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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.
Always satisfy the Prime Directive of getting the right answer above all else.

harrorm

Member

Registered: 2016-06-27

Posts: 8

Re: Need explanation on a summation transformation

Hi, yeah I figured out that one. Thanks though, but maybe you can explain this one?

How did n - 1 become n - 2 and 2^i - 1 become 2^i?

Last edited by harrorm (2016-07-07 18:19:57)

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,440

Website

Re: Need explanation on a summation transformation

It's just a re-indexing of the summation. To convince yourself, look at the first and last terms of both summations.