Question #d33ae

1 Answer
Nov 25, 2017

Use a method similar to ε-δ definition of limit.

Explanation:

Here is the definition that #a_n# diverges to infinity.:
#∀M∈R ∃N_0∈N s.t. N_0≦n → a_n>M#

It means that, if there exists #N_0# that satisfies #N_0≦n → a_n>M# for any given #M#, #a_n# diverges to #oo#.

In this sequence #C(n)=ln(n)# for a given #M#, let #N_0=e^M#.
Then, if #n>=N_0#, we can say that
#ln(n)>=ln(e^M)=M#.
Therefore, it is proven that #lim_(n->oo) ln(n)=oo#.