How did we get the general solution of $$ u=c_1c_3 \cos{(\frac{n \pi x}{l})} e^{-\frac{n^2 \pi^2 c^2 t}{l^2}}$$ to be$$ u(x,t)=\frac{1}{2}A_0+\sum_n A_n \cos{(\frac{nπx}{l})} e^{-n^2 \pi^2 c^2 t/l^2}$$
what do i already know? i know that the general solution we have written is half range cosine series. but, how can we express that u in terms of cosine series.. i tried putting n=0 and didn't get A0/2...though i got the another part by putting n from 1 to...n. Am I missing some concepts? Please remind me if I am.