>    M := 100;

M := 100

>   

>    Sum(   sin(4*n*x)/(4*n) , n=1..M)
-Sum( sin((4*n-2)*x)/(4*n-2), n=1..M)
-Sum( cos((4*n-3)*x)/(4*n-3), n=1..M)
+Sum( cos((4*n-1)*x)/(4*n-1), n=1..M);

Sum(1/4*sin(4*n*x)/n,n = 1 .. 100)-Sum(sin((4*n-2)*x)/(4*n-2),n = 1 .. 100)-Sum(cos((4*n-3)*x)/(4*n-3),n = 1 .. 100)+Sum(cos((4*n-1)*x)/(4*n-1),n = 1 .. 100)

>    partial_sum := unapply(value(%),x):

>    plot(partial_sum, -3..3);

[Maple Plot]

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