I want to prove that limn→∞(1+1f(n))g(n)=1 if f(n) grows faster than g(n) for n→∞ and limn→∞f(n)=+∞=limn→∞g(n).
It is quite easy to see that if f=g the limit is e, but I can't find a good strategy to solve this problem.
Answer
We can use that
(1+1f(n))g(n)=[(1+1f(n))f(n)]g(n)f(n)
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