Summing a Sequence: Finite or Infinite?

[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 realize 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.

 

[Mark44]

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 realize 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.

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.

 

[Firepanda]

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.

Thanks for the reply!

Does this mean it sums to infinity?

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

 

[Mark44]

Thanks for the reply!

Does this mean it sums to infinity?

Your textbook should have definitions for the terms converges and diverges.

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

I took the limit of the nth term in the sequence.