# Random stuff 2026 week 25
For what $x$ does the sequence $(\sin(x^{n} \pi))_{n=1}^{\infty}$ converge?
Now, if $|x| < 1$, then $x^{n} \pi \to 0$, and as $\sin$ is continuous, we have the sequence converging to $0$ as well.
If $x$ is an integer, then $x^{n}$ remains integer, so $\sin(x^{n}\pi) = 0$ for all $n$, and the sequence converge to $0$.
Are there other values of $x$ that makes this sequence converge? And can it converge to values other than $0$?
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Dots and boxes game, what are some heuristics to winning the game?
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Geometric proof of irrationality of $\sqrt{ 2 }$?
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I want to clone the puzzle game "heroes of sokoban", it has a lot of potential!
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Ok, how does Liouville theorem for differential algebra actually works...