# Summing a sequence

1. Jan 1, 2012

### Firepanda

I've created two summations for my coursework, now I need to show whether or not the summations are finite or infinite.

The 2 summations are very similar:

With the n/2 removed it was easy enough to show the sum was equal to 1 [edit: I now realise I may have this wrong], now with the n/2 term added I really have no idea where to start.

Any help appreciated, thanks.

Edit: I can see my writing may not be legible, 1's in the pic are straight vertical lines, some of the 2's may look like 1's, but they are 2's.

Last edited: Jan 1, 2012
2. Jan 1, 2012

### Staff: Mentor

For the first one, I found that the terms in the sequence approach a positive number. This is enough to convince me that the first series diverges.

3. Jan 1, 2012

### Firepanda

Does this mean it sums to infinity?

What were your steps to find that it approaches a positive number?

4. Jan 2, 2012

### Staff: Mentor

Your textbook should have definitions for the terms converges and diverges.
I took the limit of the nth term in the sequence.