Puzzles/Analytical Puzzles/Surprising Limit/Hint

Puzzles|Analytical puzzles | Surprising Limit|Hint

Show that

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

(calculable in head!)

HintEdit

  • Use the series expansion of e:

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

Solution

Last modified on 18 May 2007, at 16:30