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Is the series $$ \sum_{n=1}^{\infty} \sin(n^4)\sin(4^n) $$ convergent or divergent? I tried expanding the sine functions and got no clue, and any test that I know of isn't helping me with this series. ...

When I refer to the Monotone Convergence Theorem below, I refer to the very simple claim that if a non-decreasing sequence has an upper bound then it converges. I don't refer to the claim from Measure ...

There is a simple necessary and sufficient condition for a continued radical of the form $\sqrt{a_1 + \sqrt{a_2 + \dotsc}}$ to converge (where all terms $a_1, a_2$ etc. are nonnegative). Namely, that ...