Problema 2.7

Integrate[Piecewise[{{x,x<a/2},{(a-x),a/2≤x<a}},0]Sin[n Pi x/a],{x,0,a},Assumptions->{a>0,n∈Integers}]

Integrate[x Sin[n Pi x/a],{x,0,a/2},Assumptions->{a>0,n∈Integers}]

f[x_,a_,m_]:=Total[ Table[(-1)^((n-1)/2)4Sqrt[6]/(n Pi)^2Sqrt[2/a]Sin[n Pi x/a],{n,1,m,2}]]

Plot[f[x,10,41],{x,0,10}]

16 6/Pi^4//N

Sum[1/n^2,{n,1,Infinity,2}]

Manipulate[Plot[f[x,10,nMaximo],{x,0,10}],{{nMaximo,3},1,100,1}]