\documentclass[a4paper,12pt]{article}

\begin{document}

\parindent=0pt

QUESTION


Find the Taylor series for $\sinh z$ about $z=0.$



ANSWER


$f(z)=\sinh z$. Now $f(0)=0$, $f^{'}(o)=1$, $f^{''}(0)=1$ etc. so
by Taylor's Theorem $$\sinh z=z+{z^3\over 3!}+ {z^5\over
5!}+\cdots$$



\end{document}