series comparison test Watch

cooldudeman
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trying to prove it converges but I do **not** know that series of 2/sqrt(n) converges? the power is less than 1.

I did try to manipulate it differently but that also is a bit dodgy (second pic)

EDIT: added the part in ** **

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hassassin04
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(Original post by cooldudeman)
trying to prove it converges but I do know that series of 2/sqrt(n) converges? the power is less than 1.

I did try to manipulate it differently but that also is a bit dodgy (second pic)

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I think you are confusing it. The power 0<p=<1 means the sum of 1/n^p as n->infty diverges.
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BobLoblawLawBlog
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(Original post by cooldudeman)
trying to prove it converges but I do know that series of 2/sqrt(n) converges? the power is less than 1.

I did try to manipulate it differently but that also is a bit dodgy (second pic)

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You know that \frac{1}{\sqrt{n}}&gt;\frac{1}{n} and that \frac{1}{n} diverges and so \frac{1}{\sqrt{n}} must diverge. So you have shown that your series is less than a divergent one, which whilst correct isn't really much help.
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cooldudeman
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(Original post by brittanna)
You know that \frac{1}{\sqrt{n}}&gt;\frac{1}{n} and that \frac{1}{n} diverges and so \frac{1}{\sqrt{n}} must diverge. So you have shown that your series is less than a divergent one, which whilst correct isn't really much help.
yh so it diverges but the question was asking to prove that it converges...
that's why I'm confused.
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hassassin04
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(Original post by cooldudeman)
yh so it diverges but the question was asking to prove that it converges...

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Probably a misprint. The sum on pics does not converge..
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cooldudeman
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(Original post by hassassin04)
I think you are confusing it. The power 0<p=<1 means the sum of 1/n^p as n->infty diverges.
sorry I know that it diverges, that's why I am confused. its not meant to since the q was asking to prove that it converges

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BobLoblawLawBlog
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(Original post by cooldudeman)
yh so it diverges but the question was asking to prove that it converges...
that's why I'm confused.
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Are you sure it converges? Did the question ask to show it converges, or to use the comparison test to determine whether it converges or diverges? Because i'm fairly sure the series diverges.
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cooldudeman
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(Original post by brittanna)
Are you sure it converges? Did the question ask to show it converges, or to use the comparison test to determine whether it converges or diverges? Because i'm fairly sure the series diverges.
its q2, probably is just a misprint then


EDIT: oh god I wrote the question out wrong.

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