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5+..+1 2016

等差数列问题,2017*(1+2017)/2 1+2+3+.....2015+2016+2017--① 2017+2016+2015+...+3+2+1--② 由(①+②)/2

1009

(1+3+5+……+2017)-(2+4+6+……+2016) =(1-2)+(3-4)+(5-6)......+(2015-2016)+2017 =(-1)x2016/2+2017 =-1008+2017 =1009

=负2016除以2+2017=4

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

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。

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

1-2+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+3+5=3×3=9=(1+5)/2的平方.所以1++47+1++47=24²×2=1152。

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