The problem statement is-
A rod has its $x=0$ end at $0^\circ C$ and the $x=l$ end at $100^\circ C$. Now at $t>0$, we keep $x=0=l$ at $0^\circ C$. The time dependent heat equation solution is $$u=\frac{200}{\pi}\sum\frac{(-1)^{n-1}}{n}e^{-(n\pi\alpha/l)^2t}\sin\frac{n\pi x}{l}$$
Clearly, putting $t=0$ and $x=l$ should give $100^\circ C$ as given but putting $x=l$ gives $\sin(n\pi)=0$, hence the whole thing goes to $0$ instead of $100$.
What am I missing here?
A partial differential equation (PDE) is only well defined if the initial conditions (IC) and boundary conditions (BC) are compatible to each other on the whole spacetime domain $\Omega = [0,t]\times[x_a,x_b]$.
So in your case the problem (or your thinking) is not well defined.
As a hint answer the following question: Which condition has priority at $t=0$?
By the way, you have not even stated the initial condition.
Regards