Thread: Limit of a simple sequence

Prove:

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

.

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

Now show that it's monotonic, and you're finished.

Thanks allot for your help.

Quick question:

Would it not be <=?

you're working for so everything is positive.

Really I was referring to the <= n/2n = 1/2. This still holds though?

Thanks