> restart;
> simplify(integrate(cos(n*Pi*x/20)*(10-x),x=0..10));

                             cos(1/2 n Pi) - 1
                        -400 -----------------
                                   2   2
                                  n  Pi


> c:=proc(n)
>   local answer;
>   if irem(n,4)=1 then answer:=40/(n^2*Pi^2) fi;
>   if irem(n,4)=2 then answer:=80/(n^2*Pi^2) fi;
>   if irem(n,4)=3 then answer:=40/(n^2*Pi^2) fi;
>   if irem(n,4)=0 then answer:=0.0 fi;
>   RETURN(answer);
> end:
> 
> c(1);

                                 40
                                 ---
                                   2
                                 Pi

> c(1);

                                 40
                                 ---
                                   2
                                 Pi

> c(8);

                                  0

> c(31);

                               40   1
                               --- ---
                               961   2
                                   Pi

> t:=0.0:m:=10:
> plot({2.5+sum(c(n)*cos(n*Pi*x/20)*exp(-(n^2*Pi^2*t)),n=1..m)},x=0..20,y=0..20,thickness=2,color=black);

> restart;
> plots[animate](
> {2.5+sum(40*(1-cos(n*Pi/2))/(n^2*Pi^2)*
> cos(n*Pi*x/20)*exp(-(n^2*Pi^2*t)), n=1..100)},
> x=0..20,t=0..1,
> frames=50,thickness=2,color=black,view=0..11);