x Turn on thread page Beta
 You are Here: Home >< Maths

# For what positive real values of x does 1/(1^x) + 1/(2^x) + 1/(3^x)... converge? watch

1. I think that's called the Zeta function not sure though, where it goes 1/(1^x) + 1/(2^x) + 1/(3^x) 1+(4^x)... all the way to infinity.
I know it definitely converges for x>2 and it diverges for x=1, but what about the numbers between 1 and 2? I'm not that sure here. I'm assuming low values like x^1.00000001 diverge as well, but it's just a guess, since the reciprocals of primes diverge.
2. (Original post by CancerousProblem)
I think that's called the Zeta function not sure though, where it goes 1/(1^x) + 1/(2^x) + 1/(3^x) 1+(4^x)... all the way to infinity.
I know it definitely converges for x>2 and it diverges for x=1, but what about the numbers between 1 and 2? I'm not that sure here. I'm assuming low values like x^1.00000001 diverge as well, but it's just a guess, since the reciprocals of primes diverge.
When x=2 it converges to pi squared over 6. Basel problem.

Posted from TSR Mobile
3. (Original post by physicsmaths)
When x=2 it converges to pi squared over 6. Basel problem.

Posted from TSR Mobile
I've done my homework and I know that, and how Euler got the result as well. Doesn't answer my question though.
4. (Original post by CancerousProblem)
I think that's called the Zeta function not sure though, where it goes 1/(1^x) + 1/(2^x) + 1/(3^x) 1+(4^x)... all the way to infinity.
I know it definitely converges for x>2 and it diverges for x=1, but what about the numbers between 1 and 2? I'm not that sure here. I'm assuming low values like x^1.00000001 diverge as well, but it's just a guess, since the reciprocals of primes diverge.
The sum you gave (absolutely) convergences whenever

The zeta function converges (absolutely) whenever the real part of ,. However, you can write it in another way to give convergence at more values.
5. (Original post by CancerousProblem)
I've done my homework and I know that, and how Euler got the result as well. Doesn't answer my question though.
Alright, chill out.

Posted from TSR Mobile
6. (Original post by CancerousProblem)
I've done my homework and I know that, and how Euler got the result as well. Doesn't answer my question though.
You said specifically x>2 not x>=2.

Posted from TSR Mobile
7. (Original post by CancerousProblem)
I've done my homework and I know that, and how Euler got the result as well. Doesn't answer my question though.
"Doing your homework" should include googling the phrase "convergence of zeta function"!

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: February 1, 2015
Today on TSR

### Loughborough better than Cambridge

Loughborough at number one

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams