Prove:

The sequence An = 1/(n + 1) + 1/(n + 2) +...+ 1/(2n) has a limit.

Printable View

- September 10th 2009, 07:20 PMcgiulzLimit of a simple sequence
Prove:

The sequence An = 1/(n + 1) + 1/(n + 2) +...+ 1/(2n) has a limit. - September 10th 2009, 08:56 PMJG89
.

Notice that your sum has n amount of terms, and so .

Now show that it's monotonic, and you're finished. - September 10th 2009, 09:11 PMcgiulz
Thanks allot for your help. (Happy)

Quick question:

Would it not be <=? - September 11th 2009, 05:55 AMKrizalid
you're working for so everything is positive.

- September 11th 2009, 06:04 AMcgiulz
Really I was referring to the <= n/2n = 1/2. This still holds though?

Thanks