Math Is Fun Forum

b31den

Guest

Convergence Test

Hi,

I need to determine if the series 4/n(n+3) as n goes from 1 to inf diverges or converges.

Ive gotten all the way to:

4/3[ln(n) - ln(n+3)]

How do I find the value of this when I substitute in n=1 and n=inf for the proper integral?

Thanks!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Convergence Test

Hi;

If you need to do a test for convergence there are several of them and mostly they are uninteresting. More interesting and important except to your teacher probably, is to sum the series proving convergence at the same time.

Use the linearity of summation for the part in parentheses on the right.

Subtract the RHS of B from RHS of A and you get when you multiply by the 4 / 3.

Now for your question:

I see you are using the integral test as your method and have successfully done the integration. To get the value at n = ∞ will require a little cunning.

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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.
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