2
$\begingroup$

Possible Duplicate:
How to prove periodicity of $\sin(x)$ or $\cos(x)$ starting from the Taylor series expansion?

With only $f(x)=x-x^3/3!+x^5/5!-x^7/7!+ \cdots$, how to prove that $f(x)$ is periodic (there is a $k$ such that $f(x)=f(x+k)$ for all $x$) and to find a formula for $k$?

And how to prove that $f(x)$ converges for all $x$?

  • 0
    It is indeed a duplicate, feel free to delete/close2011-11-09

0 Answers 0