G3.3 Given that $f(n)=\sin \frac{n \pi}{4}$, where $n$ is an integer. If $c=f(1)+f(2)+\ldots+f(2003)$, find the value of $c$.
$$
\begin{aligned}
& f(1)+f(2)+f(3)+f(4)+f(5)+f(6)+f(7)+f(8) \\
= & \frac{1}{\sqrt{2}}+1+\frac{1}{\sqrt{2}}+0-\frac{1}{\sqrt{2}}-1-\frac{1}{\sqrt{2}}+0=0
\end{aligned}
$$
and the function repeats for every multiples of 8 .
$$
c=f(2001)+f(2002)+f(2003)=\frac{1}{\sqrt{2}}+1+\frac{1}{\sqrt{2}}=1+\sqrt{2}
$$