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5+..+1 2016

=1-1/2+1/2-1/3+1/3-1/4+...+1/2016-1/2017 =1-1/2017 =2016/2017

1-2+3-4+5-6+7-......+2015-2016=-1008 因为(1-2)=-1, 3-4=-1, ……2015-2016=-1 又,2016÷2=1008 所以,等于-1008

1/2+1/3+1/4+1/5+1/6+、、、1/2016=(1008+1007+1006+1005+、、、+3+2+1)/2016 =5536/2016=2.746

1009

(1+3+5......+2017)-(2+4+6+......+2016) =(1+2017)×1009÷2-(2+2016)×1008÷2 =2018×1009÷2-2018×1008÷2 =2018×(1009-1008)÷2 =2018÷2 =1009

=2-1+4-3+6-5+…+2016-2015 =1+1+1+…+1 =1008

1-2+3-4+5-6+7-8.......-2016+2017 =(1-2)+(3-4)+(5-6)+(7-8)+.....+(2015-2016)+2017 =-1+(-1)+(-1)+(-1)+.....+(-1)+2017 =-1*2016/2+2017 =-1008+2017 =1009

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 ×{2015/201...

2+4+6+8+....2017-1+3+5+...+2016 =2+3+4+...+2017-1 =[(2+2017)x2016]/2-1 =2019x1008-1 =2035152-1 =2035151。

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