1/(2*4)+1\(4*6)+1\(6*8)+.+1\(48*50)简便计算

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1/(2*4)+1\(4*6)+1\(6*8)+.+1\(48*50)简便计算

1/(2*4)+1\(4*6)+1\(6*8)+.+1\(48*50)简便计算
1/(2*4)+1\(4*6)+1\(6*8)+.+1\(48*50)简便计算

1/(2*4)+1\(4*6)+1\(6*8)+.+1\(48*50)简便计算
1/(2*4)+1\(4*6)+1\(6*8)+.+1\(48*50)
=1/2×(1/2-1/4)+1/2×(1/4-1/6)+1/2×(1/6-1/8)+.+1/2×(1/48-1/50)
=1/2×(1/2-1/4+1/4-1/6+1/6-1/8+.+1/48-1/50)
=1/2×(1/2-1/50)
=1/2×24/50
=6/25

=1/2[(1/2-1/4)+(1/4-1/6)+……+(1/48-1/50)]
=1/2(1/2-1/50)
=6/25=0.24