(1/8+1/24+1/48+1/80+1/120+1/168)简便计算

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(1/8+1/24+1/48+1/80+1/120+1/168)简便计算

(1/8+1/24+1/48+1/80+1/120+1/168)简便计算
(1/8+1/24+1/48+1/80+1/120+1/168)简便计算

(1/8+1/24+1/48+1/80+1/120+1/168)简便计算
1/8+1/24+1/48+1/80+1/120+1/168
=1/2*[(1/2-1/4)+(1/4-1/6)+(1/6-1/8)+(1/8-1/10)+(1/10-1/12)+(1/12-1/14)]
=1/2*[1/2-1/14]
=3/14
能看懂吧,

1/8=(1/2)*(1/2-1/4)
1/24=(1/2)*(1/4-1/6)
……
1/168=(1/2)*(1/12-1/14)
原式=(1/2)*[(1/2-1/4)+(1/4-1/6)+……+(1/12-1/14)]
=(1/2)*[1/2-(1/4-1/4)-……-(1/12-1/12)-1/14]
=(1/2)*(1/2-1/14)
=(1/2)*(6/14)
=3/14

(1/8+1/24+1/48+1/80+1/120+1/168)
=(1/2*4+1/4*6+1/6*8+1/8*10+1/10*12+1/12*14)
=1/2*(1/2-1/4+1/4-1/6+......+1/12-1/14)
=1/2(1/2-1/14)
=3/28