(1/8+1/24+1/48+1/80+1/120+1/168+1/224)*64=?简便算法

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(1/8+1/24+1/48+1/80+1/120+1/168+1/224)*64=?简便算法

(1/8+1/24+1/48+1/80+1/120+1/168+1/224)*64=?简便算法
(1/8+1/24+1/48+1/80+1/120+1/168+1/224)*64=?
简便算法

(1/8+1/24+1/48+1/80+1/120+1/168+1/224)*64=?简便算法
观察单项:
1/8=(1/2-1/4)/2
1/24=(1/4-1/6)/2
1/48=(1/6-1/8)/2
1/80=(1/8-1/10)/2
1/120=(1/10-1/12)/2
1/168=(1/12-1/14)/2
1/224=(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

(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