Puzzles/Analytical Puzzles/Surprising Limit/Hint

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Puzzles|Analytical puzzles | Surprising Limit|Hint

Show that

\lim_{n\rightarrow\infty}n\sin(2\pi n!e)=2\pi.

(calculable in head!)

Hint[edit]

  • Use the series expansion of e:

e=1+\frac{1}{2}+\frac{1}{3!}+\frac{1}{4!}+...

Solution