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Help! Convergence? watch

1. So I'm trying to find out if this is convergent or divergent.

By the comparison test, I found out that this is divergent, but then with the divergence test, I find it's convergent.
2. Does converge or diverge?
3. (Original post by Noble.)
Does converge or diverge?
It's a p series with p<=1 so it diverges, and thus so does the original sum.
That's what I did in the comparison test.

But then when I took the limit to infinity of the original sum, I got 0.
So wouldn't that mean it converges by the divergence test?
4. (Original post by eterna)
It's a p series with p<=1 so it diverges, and thus so does the original sum.
That's what I did in the comparison test.

But then when I took the limit to infinity of the original sum, I got 0.
So wouldn't that mean it converges by the divergence test?
does not imply is finite, for example, as you've just said yourself is not finite, yet .
5. (Original post by Noble.)
does not imply is finite, for example, as you've just said yourself is not finite, yet .
oh ok thanks, you're right; doesn't necessarily imply convergence. Should have realized that while doing the comparison test.
6. (Original post by eterna)
oh ok thanks, you're right; doesn't necessarily imply convergence. Should have realized that while doing the comparison test.
does not imply exists

However,

exists implies

That might be where you got confused.
7. (Original post by Noble.)
does not imply exists

However,

exists implies

That might be where you got confused.
Thanks!
I have another question
How would you go about showing that is convergent?
8. (Original post by eterna)
Thanks!
I have another question
How would you go about showing that is convergent?
I assume you mean from and not from , however this isn't convergent, via the comparison test. If you need a hint:

the inequality is strict for
9. (Original post by Noble.)
I assume you mean from and not from , however this isn't convergent, via the comparison test. If you need a hint:

the inequality is strict for
ah yeah, I meant from n=1. thanks!
10. (Original post by eterna)
Thanks!
I have another question
How would you go about showing that is convergent?
Are you sure that converges???
11. (Original post by davros)
Are you sure that converges???
It doesn't.

So by comparison, it diverges.

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