1/2+1/8+1/24+1/48+1/80要简便哦

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1/2+1/8+1/24+1/48+1/80要简便哦1/2+1/8+1/24+1/48+1/80要简便哦1/2+1/8+1/24+1/48+1/80要简便哦1/2+1/8+1/24+1/48+1/80

1/2+1/8+1/24+1/48+1/80要简便哦
1/2+1/8+1/24+1/48+1/80
要简便哦

1/2+1/8+1/24+1/48+1/80要简便哦
1/2+1/8+1/24+1/48+1/80
=1/1*2+1/2*4+1/4*6+1/6*8+1/8*10
=1/2*(1-1/2+1/2-1/4+……+1/8-1/10)
=1/2*(1-1/10)
=1/2*9/10
=9/20

=1/2+1/2*4+1/4*6+1/6*8+1/8*10
=1/2+(1/2)*(1/2-1/4)+(1/2)*(1/4-1/6)+(1/2)*(1/6-1/8)+(1/2)*(1/8-1/10)
=1/2+(1/2)*(1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10)
=1/2+(1/2)*(1/2-1/10)
=1/2+1/5
=7/10

=1/2+1/4*(1/2+1/6+1/12+1/20)
=1/2+1/4*(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5)
=1/2+1/4*4/5
=1/2+1/5
=7/10

1/2+1/8+1/24+1/48+1/80
=1/2+(1/2)*[(1/2-1/4)+(1/4-1/6)+(1/6-1/8)+(1/8-1/10)]
=1/2+(1/2)*(1/2-1/10)
=1/2+(1/2)*(2/5)
=1/2+1/5
=7/10