1/(1×3)+1/(2×4)+1/(3+5)……+1/(2016x2018)
= 1/2×{1-1/3+1/2-1/4+1/3-1/5+.....1/2016-1/2018}
= 1/2 ×{1-1/3+1/3-1/5+.....1/2015-1/2017} + 1/2×{1/2-1/4+1/4-1/6+.....1/2016-1/2018}
= 1/2 ×{1-1/2017} + 1/2×{1/2-1/2018}
= 1/2 ×{2015/2017} + 1/2×{1008/2018}
= 2015/4034 + 252/1009
= (2033135+1016568)/4070306
= 3049703/4070306
= 1/2×{1-1/3+1/2-1/4+1/3-1/5+.....1/2016-1/2018}
= 1/2 ×{1-1/3+1/3-1/5+.....1/2015-1/2017} + 1/2×{1/2-1/4+1/4-1/6+.....1/2016-1/2018}
= 1/2 ×{1-1/2017} + 1/2×{1/2-1/2018}
= 1/2 ×{2015/2017} + 1/2×{1008/2018}
= 2015/4034 + 252/1009
= (2033135+1016568)/4070306
= 3049703/4070306
温馨提示：内容为网友见解，仅供参考
第1个回答 2016-10-07
1/(1×3)+1/(2×4)+1/(3+5)……+1/(2016x2018)
=1/2×（1/1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+...+1/2015-1/2017+1/2016-1/2018)
=1/2×（1/1+1/2-1/2017-1/2018)
=1/2×（2017×2018+2017×2018/2-2018-2017)/（2017×2018）
=1/2×6101424/4070306
=6101424/8140612
=1525356/2035153
=1/2×（1/1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+...+1/2015-1/2017+1/2016-1/2018)
=1/2×（1/1+1/2-1/2017-1/2018)
=1/2×（2017×2018+2017×2018/2-2018-2017)/（2017×2018）
=1/2×6101424/4070306
=6101424/8140612
=1525356/2035153
第2个回答 2016-10-07
原式
=0.5*（1/1-1/3+1/3-1/5+1/5-1/7+......+1/2016-1/2018）
=0.5*（1/1-1/2018）
=2017/4036
=0.5*（1/1-1/3+1/3-1/5+1/5-1/7+......+1/2016-1/2018）
=0.5*（1/1-1/2018）
=2017/4036
第3个回答 2016-10-07
解：
1/(1×3)+ 1/(2×4)+ 1/(3×5)+...+1/(2016×2018)
=½×(1- 1/3 +1/2 -1/4 +1/3 -1/5+...+1/2016 -1/2018)
=½×[(1+ 1/2+ 1/3+...+1/2016)-(1/3 +1/4 +1/5+...+1/2018)]
=½×(1+ 1/2 -1/2017 -1/2018)
=1525356/2035153
1/(1×3)+ 1/(2×4)+ 1/(3×5)+...+1/(2016×2018)
=½×(1- 1/3 +1/2 -1/4 +1/3 -1/5+...+1/2016 -1/2018)
=½×[(1+ 1/2+ 1/3+...+1/2016)-(1/3 +1/4 +1/5+...+1/2018)]
=½×(1+ 1/2 -1/2017 -1/2018)
=1525356/2035153
第4个回答 2016-10-07
=(1-1/2018)×1/2
=2017/4036追答
=2017/4036追答
--------看错了，改：
1/(1×3)+1/(2×4)+1/(3+5)……+1/(2016x2018)
=(1-1/2017)×1/2+(1/2-1/2018)×1/2
=1008/2017+252/1009
=
=1525356/2035153
≈0.7495
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