Question

Does `a_n = [n(n+1)]/(n+sqrt(n))` converge?

Answer 1

No

Explanation:

Because `a_"n"` is a functionnal sequence you only have to study limits ( if there's any) in `+oo` : #lim_"n->+oo"a_"n"= lim_"n->+oo"(n(n+1)) /(n+sqrt(n))#
`≈_"+oo"(n²)/n=n`

So
`lim_"n->+oo"a_"n"=+oo`
So no, `a_"n"` doesn't converge.
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