\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Expand the series for \(\sin(x)=\displaystyle\sum_{k=0}^\infty \frac{(-1)^k x^{2k+1}}{(2k+1)!}\) up to the term of order 5.
\(\sin(x)=\)
\(+\displaystyle\sum_{k=3}^\infty \frac{(-1)^k x^{2k+1}}{(2k+1)!}\)