The solution of a PDE can be represented by a Fourier cosine series $ u(x,t)=\sum_{n=1}^\infty A_n(t)\cos\frac{n\pi x}L. $
Applying a given initial condition
$ u(x,0)=100, $
lets us solve for $A_n(0)$ through the orthogonality of cosines:
$\begin{align} u(x,0)&=\sum_{n=1}^\infty A_n(0)\cos\frac{n\pi x}L=100\\ &\Rightarrow A_n(0)=\frac{400}L\int_0^L\cos\frac{n\pi x}L\,dx=0. \end{align}$
This does not seem correct, however. What am I doing wrong?