答：
在0~2π周期内：
sin(π/4)+sin(2π/4)+sin(3π/4)+sin(4π/4)+.+sin(8π/4)=0
100/8=12余4
f(x)=sin(πx/4)
f(0)+f(1)+f(2)+.+f(100)
=sin0+sin(π/4)+sin(2π/4)+sin(3π/4)+.+sin(100π/4)
=0+0+.+sin(97π/4)+sin(98π/4)+sin(99π/4)+sin(100π/4)
=sin(π/4)+sin(2π/4)+sin(3π/4)+sin(4π/4)
=√2/2+2+√2/2+0
=2+√2