Help - Derivation of formula for Pi (4 Viewers)

[seanieg89]

Ok so what I need to do to fix this, is:

1) Consider domain of Alpha, I am allowed to restrict it to 0 to pi right? because that is the only alpha that I will ever deal with?

2) Consider all the cases of cos2ntheta in this domain.

3) Find inequalities for all these cases?

Would that fix it?

Well yeah alpha is between 0 and pi always. Not sure what you mean by cases of cos2ntheta though. Whatever case argument you try be very careful with the inequalities and try not to skip steps. I am not that confident in it working but I don't have to time to try it myself right now.

 

[Sy123]

Okay, well investigating the inequality for a bit, I found that I was a bit too hasty in establishing it and there are just way too many holes and that it is completely wrong and if I try to fix I end up with J=0 (without any influence from n) which isn't good. So I don't think Squeeze theorem won't work.



Now I need to show that for each of them as n approaches infinity the integral converges to zero. We can already say that about the middle term, so we just need to concentrate on the first term and the last term.

So...how do I do this? =(
What are some ways of proving an integral is convergent?

 

[seanieg89]

Okay, well investigating the inequality for a bit, I found that I was a bit too hasty in establishing it and there are just way too many holes and that it is completely wrong and if I try to fix I end up with J=0 (without any influence from n) which isn't good. So I don't think Squeeze theorem won't work.



Now I need to show that for each of them as n approaches infinity the integral converges to zero. We can already say that about the middle term, so we just need to concentrate on the first term and the last term.

So...how do I do this? =(
What are some ways of proving an integral is convergent?

As I expected.

And in your expression now you have split up your alpha integral in an illegal way, your first integral is nonconvergent, and so must be your third. Its like writing:



the first and second term here don't even make sense, much like the first and third term don't make sense in what you have just written.

The analysis of your expression I is a little more delicate than you seem to think.

 

[Sy123]

As I expected.

And in your expression now you have split up your alpha integral in an illegal way, your first integral is nonconvergent, and so must be your third. Its like writing:



the first and second term here don't even make sense, much like the first and third term don't make sense in what you have just written.

The analysis of your expression I is a little more delicate than you seem to think.

Alright then, I will just leave this problem alone for now, maybe I'll come back to it later. I still want to use this integral approach
Thanks for the help man, really appreciate it, and excuse any mathematical garbage that is contained within these posts