Why do computer programs (Wolfram Alpha, Symbolab) think $\sum_{n=0}^{\infty} \sin(\frac{\pi}{2}n!)$ is divergent? I've been recently looking at the series
$$\sum_{n=0}^{\infty} \sin(\frac{\pi}{2}n!)=1+1+0+0+0+0+0+\cdots,$$
which should equal $2$. However, programs such as Wolfram Alpha, Symbolab, etc., tell me that this series is divergent. Can someone explain what's happening?

Apparently, the software isn't clever enough to get the trick here.  I suspect that when Wolfram Alpha says the series is divergent, what it really means is that it is unable to determine that the series is convergent.  
