公务员数学运算题一道

D。11/451/(1×2×3)=[1/(1×2)-1/(2×3)]/21/(2×3×4)=[1/(2×3)-1/(2×3)]/21/(3×4×5)=[1/(3×4)-1/(4×5)]/21/(4×5×6)=[1/(4×5)-1/(5×6)]/2。1/(8×9×10)=[1/(8×9)-1/(9×10)]/2所以1/(1×2×3)+1/(2×3×4)+…+1/（8×9×10）=[1/(1×2)-1/(2×3)]/2+[1/(2×3)-1/(2×3)]/2+[1/(3×4)-1/(4×5)]/2+[1/(4×5)-1/(5×6)]/2+。。。+[1/(8×9)-1/(9×10)]/2=[1/(1×2)-1/(2×3)+1/(2×3)-1/(2×3)+1/(2×3)-1/(2×3)+1/(3×4)-1/(4×5)+1/(4×5)-1/(5×6)+。。。+1/(8×9)-1/(9×10)]/2=[1/(1×2)-1/(9×10)]/2=(1/2-1/90)/2=(44/90)/2=22/90=11/45