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series comparison test

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 ** **

Posted from TSR Mobile

(edited 10 years ago)

1385080404625.jpg35.8KB

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Reply 1

hassassin04

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)

Posted from TSR Mobile

I think you are confusing it. The power 0<p=<1 means the sum of 1/n^p as n->infty diverges.

(edited 10 years ago)

Reply 2

BobLoblawLawBlog

Original post by cooldudeman

You know that

\frac{1}{\sqrt{n}}>\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.

Reply 3

cooldudeman

Original post by brittanna

You know that

\frac{1}{\sqrt{n}}>\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.
Posted from TSR Mobile

(edited 10 years ago)

Reply 4

hassassin04

Original post by cooldudeman

yh so it diverges but the question was asking to prove that it converges...

Posted from TSR Mobile

Probably a misprint. The sum on pics does not converge..

Reply 5

cooldudeman

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

Posted from TSR Mobile

Reply 6

BobLoblawLawBlog

Original post by cooldudeman

yh so it diverges but the question was asking to prove that it converges...
that's why I'm confused.
Posted from TSR Mobile

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.

(edited 10 years ago)

Reply 7

cooldudeman

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.