Math Is Fun Forum

genericname

Member

Registered: 2012-05-16

Posts: 52

Question about testing for convergence/divergence

When should I use the comparison test? What indications should I look out for?

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Question about testing for convergence/divergence

Hi genericname

I usually always start from the ratio test, root test, comparison test, etc. You just try any one and if you don't get a result you try another one.

http://www.mathisfunforum.com/viewtopic.php?id=17887

Last edited by anonimnystefy (2012-07-03 10:35:43)

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Question about testing for convergence/divergence

Hi genericname;

Welcome to the forum! It is a matter of experience and sometimes taste.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

genericname

Member

Registered: 2012-05-16

Posts: 52

Re: Question about testing for convergence/divergence

Thanks for the replies. One question about a problem: Why does (ln(n))/(n) approximately equal to 1/n? In the book I'm using, the author compares (ln(n))/(n) with 1/n. What happens to the ln?

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Question about testing for convergence/divergence

That is not a great approximation. How is he comparing the two expressions?

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Question about testing for convergence/divergence

Hi genericname;

What book?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.