n=1时公式成立；现在假设对n-1公式成立那么sinx+sin2x+sin3x+……+sinnx=sinx+sin2x+sin3x+……+sin(n-1)x+sinnx=[sin((n-1)x/2)sin(nx/2)]/sin(x/2)+sinnx=[sin((n-1)x/2)sin(nx/2)+sinnxsin(x/2)]/sin(x/2)=sin(nx...