anyone know anything about fibonacci sequence and limits?

such as..

State the limit of each sequence, if it exists. If it does not, explain why.

a) 1, 1, 2, 3, 5, 8, 13, 21, 34, 55...

b) 1, 2, 3/2, 5/3, 8/5, 13/8, 21/13,34/21, 55/34...

i thought the fibonacci sequence didnt have a limit, but ive been researching it for a while and people get very confusing with their explanations of it.