(1/8+1/24+1/48+1/80+1/120+1/168+1/224)*64=?简便算法
问题描述：
(1/8+1/24+1/48+1/80+1/120+1/168+1/224)*64=?
简便算法
答
(1/8+1/24+1/48+1/80+1/120+1/168+1/224)*64
=(1/2-1/4+1/4-1/6+....+1/14-1/16)/2*64
=(1/2-1/16)*32
=5/16*32
=10
答
观察单项：1/8=(1/2-1/4)/21/24=(1/4-1/6)/21/48=(1/6-1/8)/21/80=(1/8-1/10)/21/120=(1/10-1/12)/21/168=(1/12-1/14)/21/224=(1/14-1/16)/2提出来1/2；括号内很容易求和；即：（1/2-1/16）*64/2=16-2=14...