Hey,

I am having trouble with the following proof.

If Pj = ∑ Qj (limits i = j+1 to ∞), then how do you prove that : ∑ Pj (limits 0 to ∞) = ∑ j*Qj (limits j+1 to ∞)

Cheers.

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- Mar 2nd 2013, 06:03 PMbankerHelp with Summations
Hey,

I am having trouble with the following proof.

If Pj = ∑ Qj (limits i = j+1 to ∞), then how do you prove that : ∑ Pj (limits 0 to ∞) = ∑ j*Qj (limits j+1 to ∞)

Cheers. - Mar 2nd 2013, 09:32 PMMacstersUndeadRe: Help with Summations
If

$\displaystyle P_j = \sum\limits_{i=j+1}^\infty Q_i$, then

$\displaystyle \sum\limits_{j=0}^\infty P_j = \sum\limits_{j=0}^\infty (\sum\limits_{i=j+1}^\infty Q_i)= (\sum\limits_{i=1}^\infty Q_i) + (\sum\limits_{i=2}^\infty Q_i) + ... + (\sum\limits_{i=j+1}^\infty Q_i)$

If you can show $\displaystyle (\sum\limits_{i=1}^\infty Q_i) = (\sum\limits_{i=2}^\infty Q_i) = ... = (\sum\limits_{i=j+1}^\infty Q_i)$ then you are done (since there are j terms in the sum). Otherwise I'm stumped. - Mar 3rd 2013, 07:24 AMbankerRe: Help with Summations
Cheers man, managed to do it. Same logic but a different intermediary step!

- Mar 3rd 2013, 10:23 AMMacstersUndeadRe: Help with Summations
I'm curious to what the different intermediary step is.