Math Question (I'm a jackass)

[MisterPants]

I'm screwing something up when I manipulate Euler's Zeta Function. Somebody tell me what it is. I'll be using Z for zeta(s), and when i type 1/n assume i mean 1/n^s where s >1.

A better version:
Z=1+1/2+1/3...
Z/2=1/2+1/4+1/6...
Z-Z/2=1+1/3+1/5+1/7...
Z-Z/2=Z(1-1/2)=Z/2

Thus:
1+1/3+1/5+1/7...=1/2+1/4+1/6+1/8...

1/3(Z-Z/2)=1/3+1/9+1/15...
Z-Z/2-(Z-Z/2)/3=1+1/5+1/7+1/11...

Can somebody show me how to get 1/Pi(1-p^-s)=Sigma(n^-s)

(Pi being the multiplicative analog of Sigma, n being the natural numbers, and p being the primes)

 

[bootymac]

 

[Gunslinger08]

Why the hell are you doing this at 2 in the morning?

 

[MrYogi]

1/3(Z-1/2Z)=1/3+1/9+1/15... should be (Z-1/2Z)/3=1/3+1/9+1/15...

 

[edro]

Originally posted by: joshsquall
Why the hell are you doing this at 2 in the morning?

Could I ask you some of my UNIX homework questions.... I am doing it at 2am as well!

 

[edro]

Here is some of mine...

"Can a measure of whether a process is likely to be CPU bound or I/O bound be determined by analyzing source code? How can this be determined at run time?"

 

[MisterPants]

This isn't homework. My Math Teacher/Math Team Coach thought I'd find it interesting, and I want to know why I can't get the result I should be getting.


Yogi: Aren't those expressions equivalent? It reads like (1/x) * 2 should be 2/x to me. Or is it an unfunny joke?

 

[GoingUp]

Originally posted by: bootymac

 

[Gunslinger08]

Ahh, math team. I did that stuff back in middle/high school.

 

[MrYogi]

Originally posted by: MisterPants
This isn't homework. My Math Teacher/Math Team Coach thought I'd find it interesting, and I want to know why I can't get the result I should be getting.


Yogi: Aren't those expressions equivalent? It reads like (1/x) * 2 should be 2/x to me. Or is it an unfunny joke?

(1/3)(Z-1/2Z) This is correct
1/3(Z-1/2Z) this looks like 1/(3z-3/2z)

Anyway, thats minor. I will look at the problem again before going to sleep. thanks

 

[MisterPants]

Originally posted by: MrYogi

Originally posted by: MisterPants
This isn't homework. My Math Teacher/Math Team Coach thought I'd find it interesting, and I want to know why I can't get the result I should be getting.


Yogi: Aren't those expressions equivalent? It reads like (1/x) * 2 should be 2/x to me. Or is it an unfunny joke?

(1/3)(Z-1/2Z) This is correct
1/3(Z-1/2Z) this looks like 1/(3z-3/2z)

Anyway, thats minor. I will look at the problem again before going to sleep. thanks

Thanks, I hadn't considered that. I've changed it in the original post.

 

[MrYogi]

Also, the last line Z-1/2Z-1/3(1-1/2Z)=1+1/5+1/7+1/11...
should be Z-1/2Z-1/3(Z-1/2Z)=1+1/5+1/7+1/11...

 

[MrYogi]

Sorry for being a pest. 1/2Z actually looks like 1/(2Z).

A better version:
x=1+1/2+1/3...
x/2=1/2+1/4+1/6...
x-x/2=1+1/3+1/5+1/7...
x-x/2=x(1-1/2)=x/2

Thus:
1+1/3+1/5+1/7...=1/2+1/4+1/6+1/8...

1/3(x-x/2)=1/3+1/9+1/15...
x-x/2-1/3(x-x/2)=1+1/5+1/7+1/11...

Can somebody show me how to get 1/Pi(1-1/p^s)=Z(s)?

 

[StatisticianOG]

z(s)(1-2^-s) = (1+1/2^s+1/3^s+...)(1-2^-s) =
(1+1/2^s+1/3^s+...)-(1/2^s+1/4^s+1/6^s+...) =
z(s)(1-2^-s)(1-3^-s) =
(1+1/3^s+1/5^s+1/7^s)-(1/3^s+1/9^s+1/15^s+...) =
z(s)(1-2^-s)(1-3^-s)...(1-p_n^-s)..etc.. =
z(s)*PI(1-p_n^-s)[n=1 to oo] = 1,

and the result follows.

 

[AgaBoogaBoo]

Are we still talking in the english language? This is what stuff sounded like when I frst came to this website, blah balh blah...

 

"Are we still talking in the english language? This is what stuff sounded like when I frst came to this website, blah balh blah..."

Yeah, there was a time when people would post their math problems, including puzzles, so often. I enjoyed it a lot. But then I guess people were whining too much about people posting their homeworks, and things just changed. Now my brain is fried . . . I can't even have the motivation to try math problems anymore. *Sigh!*

Sorry Mister Pants, but my brain won't take this problem at the moment. I'm not about to refresh my memory. Hope Mr. Yogi and StatisticianOG were helpful to you.