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Prove that $\sum\limits_{n=1}^\infty \frac{4^n}{1 +2^n}$ converges
Prove that the series $\sum\limits_{n=1}^\infty \frac{4^n}{1 +2^n}$ converges.
The problem is quite easy to me, since the terms of the series are not in ratio 4 : 1, but I just can't figure out how to approach this sort of problem.
The natural way seems to be to verify if there is a subsequence convergent to a value less than or equal to one, but I can't see any.
Maybe I can approach this by the comparison test, but can someone explain how to do it in the first place?
Any other way to approach this problem is appreciated.
A:
By using the fact that $a^n > a^{n-1} + 0b46394aab
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