The proof of the first higher number: if an > 0 and lim (n →∞) a (n + 1) / a (n) = a, then LIM (an ^ (1 / N)) = a Is there a simpler proof

The proof of the first higher number: if an > 0 and lim (n →∞) a (n + 1) / a (n) = a, then LIM (an ^ (1 / N)) = a Is there a simpler proof

Using Stolz Theorem is the simplest way
The conclusion is obvious~
If we don't use Stolz Theorem, it's not difficult~
lim(n→∞)a(n+1)/a(n)=a
By definition:
For any ε > 0, there exists n > 0. When n > N, there is | a (n + 1) / a (n) - A|

Elden Ring Premiere

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