Question

2, 4, 6, 8, 10
I know this diverges but what is the limit?

Also, is there a limit with numbers that repeat? (ie: -1,1,-1,1...(-1)^n)

Answer 1

1. You are right, this sequence diverges (or converges to infinity) so

$\lim_{n\to\infty}\,2n=\infty$

2. In this case limit does not exist.