Thread: proving the limit

Consider the sequence
{√n(√(n + 1)-√n)} where n>=1 . If the limit exists, find it using ideas
from first year, and then carefully prove that the limit is indeed your choice. If not, prove
that the limit does not exist.
Using first year ideas i found the limit to be 0. I am still working on the question but not really getting anywhere.. Any help would be nice

The limit is not 0.

Yea you are right it is 0.5.. How can I prove that it is upper bounded because that seems like the best way to prove it converges