Question

Question #d33ae

Answer 1

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`.