Question

(1X5)/2008+(5X9)/2008+(9X13)/2008+······+(55X59)/2008=?用简便方法

Answer 1

提取出来2008后,1/（1x5）=(1-1/5)/4,1/(5x9)=(1/5-1/9)/4等,在提取1/4,1-1/5+1/5-1/9=1/9-1/13.-1/59=1-1/59=4/59.最后原式等于2008x1/4x4/59=2008/59