The limit is not 0.
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