Does converge, and if so to what value?

I'm not too sure how to go about this question, any help would be greatly appreciated!

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- Mar 30th 2011, 10:42 AMusagi_killerConvergence
Does converge, and if so to what value?

I'm not too sure how to go about this question, any help would be greatly appreciated! - Mar 30th 2011, 11:25 AMchisigma
The Swiss mathematician Leonhard Euler demonstrated two and half centuries ago that the series...

... diverges, so that diverges also the product...

Kind regards

- Mar 30th 2011, 11:50 AMFernandoRevilla
However, if then,

So, can extend the formula,

- Mar 30th 2011, 10:08 PMusagi_killer
@chisigma thanks for the help! however I am still a bit unsure on how the divergence of the sum implies that the product also diverges?

@FernandoRevilla cheers for that! I haven't seen that formula yet, nor can I find it in my notes, however im very interested, can you perhaps show me a proof of how the formula comes about?

thanks again! - Mar 30th 2011, 10:41 PMFernandoRevilla
- Mar 31st 2011, 03:13 AMchisigma
In...

Convergence of Infinite Products « The Everything Seminar

... there is the proof of the following theorem:*an 'infinite product' of the form...*...

... converges if and only if the 'infinite sum'...

... converges

Kind regards

- Mar 31st 2011, 03:57 AMusagi_killer
Thanks guys! Makes sense now!