Do These Complex Sequences Converge?

[kathrynag]

Homework Statement

I need to find if sequences have limits
1. 1,i,-1,-i,1,i,-i,1...
2. 1,i/2,-1/3,-i/4,1/5...
3. (1+i)/2,...,[(1+i)/2]^n
4.3+4i/5,...[(3+4i)/5]^n

Homework Equations

The Attempt at a Solution

I say 1 and 2 don't have limits because of the sign changes.
I say 3 and 4 have limits, but am not sure on how to find them.
3.1/2+1/2i
4.?

 

[Office_Shredder]

What tests do you have to determine if a sequence converges or not? e.g. see if it's Cauchy. Write down some, and see if they apply