lg(100sinπ/4)=2-1/2*lg2,┄┄lg(100sin^n*π/4）=2-n/2*lg2,为公差q=-1/2lg2的等差数列,前几项的和最大,每项大于等于零,则2-n/2*lg2≥0,∵lg2=0.30103 ,∴n≤4/lg2=13.28,∵n为整数,∴前13项的和最大=[2-1/2*lg2+2-1/2*lg2-(13-1)/2*lg2]*13/2=26-91/2*lg2.