计算:1/a(a+2)+1/(a+2)(a+4)+1/(a+4)(a+6)=
计算:1/a(a+2)+1/(a+2)(a+4)+1/(a+4)(a+6)=
原式=[1/a-1/(a+2)]/2+[1/(a+2)-1/(a+4)]/2+[1/(a+4)-1/(a+6)]/2
=[1/a-1/(a+2)+1/(a+2)-1/(a+4)+1/(a+4)-1/(a+6)]/2
=[1/a-1/(a+6)]/2
={[(a+6-1)]/[a(a+6)]}/2
={(a+5)/[a(a+6)]/2
=(a+5)/[2a(a+6)]
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计算2/a(a+2)+2/(a+2)(a+4)+2/(a+4)(a+6)+2/(a+6)(a+8)
2/a(a+2)+2/(a+2)(a+4)+2/(a+4)(a+6)+2/(a+6)(a+8)=【1/a-1/(a+2)】+【1/(a+2)-1/(a+4)】+【1/(a+4)-1/(a+6)】+【1/(a+6)-1/(a+8)】=1/a-1/(a+2)+1/(a+2)-1/(a+4)+1/(a+4)-1/(a+6)+1/(a+6)-1/(a+8)=1/a-1/（a+8)=8/【a（a+8）】 望采纳
计算1/ab+1/(a+2)(b+2)+1/(a+4)(b+4)+.1/(a+2012)(b+2012),其中a,b满足|ab-8|+|2-a|=0
ab-8=0 2-a=0 得 a=2 b=4
原式=1/(2*4)+1/(4*6)+1/(6*8)+...+1/(2014*2016)
=1/2*(1/2-1/4)+1/2*(1/4-1/6)+...+1/2*(1/2014-1/2016)
=1/2*[1/2-1/4+1/4-1/6+...+1/2014-1/2016]
=1/2*[1/2-1/2016]
=(1008-1)/(2*2016)
=1007/4032
a=1,b=3,求1/ab+1/(a+2)(b+2)+1/(a+4)(b+4)+.1/(a+100)(b+100)的值。
若a=1，b=3，则：
1/ab+1/(a+2)(b+2)+1/(a+4)(b+4)+.......1/(a+100)(b+100)
＝1/(1*3) +1/(3*5) +1/(5*7) +...+1/(99*101) +1/(101*103)
=(1/2)*[(1-1/3)+(1/3 -1/5)+(1/5 -1/7)+...+(1/99 -1/101)+(1/101 -1/103)]
=(1/2)*(1-1/103)
=51/103
已知|ab-8|+|2-a|=0,求1/ab+1/(a+2)(b+2)+1/(a+4)(b+4)+.+1/(a+2012)(b+2012)
|ab-8|+|2-a|=0
∴ab=8
a=2
∴b=4
1/ab+1/(a+2)(b+2)+1/(a+4)(b+4)+.......+1/(a+2012)(b+2012)
=1/(2*4)+1/(4*6)+1/(6*8)......+1/(2014*2016)
=1/2*(1/2-1/4)+1/2(1/4-1/6)+1/2*(1/6-1/8)+.....+1/2(1/2014-1/2016)
=1/2(1/2-1/4+1/4-1/6+1/6-1/8+.......+1/2014-1/2016)
=1/2*(1/2-1/2016)
=1007/4032
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ab-3的绝对值与b-1绝对值互为相反数1/ab+1/(a+2)(b+2)+1/(a+4)(b+4)+1/(a+6)（b+6）.+1/（a+2010）b+2010
∵ab-3的绝对值与b-1绝对值互为相反数,
∴ab-3=0 b-1=0
a=3 b=1
解：原式=1/ab+1/(a+2)(b+2)+1/(a+4)(b+4)+1/(a+6)（b+6）...+1/（a+2010）（b+2010）
=1/2×（1-1/3+1/3-1/5+……+1/2011-1/2013）
=1/2×2012/2013
=1006/2013
若有理数a b 满足|a-1|+（b-3）^2=0,试求 1/ab+1/(a+2)(b+2)+1/(a+4)(b+4)……+1/(a+100)(b)
a=1
b=3
原式=1/3+1/3x5+1/5x7+.........+1/101x103
因为分子都是1 分母相差2
最后分子上变成2了 所以得乘以1/2
肯定要表示成最后能合并同类项的分式
比方1/3x5=1/2x(1/3-1/5)
同理1/5x7=1/2x(1/5-1/7)
...............................
最后只剩下首尾两项了1/2x（1-1/103）=51/103
计算1/a(a+1)+1/(a+1)(a+2)+.+1/(a+2007)(a+2008)
列项,
1/a(a+1)+1/(a+1)(a+2)+...+1/(a+2007)(a+2008)
=1/a-1/(a+1)+1/(a+1)-1/(a+2)..-1/(a+2008)
=1/a-1/(a+2008)
=2008/(a*(a+2008))
计算1/(2*4)+1/(4*6)+1/(6*8)+.+1/(98*100).
1/(2*4)
=(1/2-1/4)/2
1/(4*6)
=(1/4-1/6)/2
......
1/(98*100)
=(1/98-1/100)/2
1/(2*4)+1/(4*6)+1/(6*8)+...+1/(98*100)
=1/2(1/2-1/4+1/4-1/6....+1/98-1/100)
=1/2*(1/2-1/100)
=1/2*49/100
=49/200
计算1/a(a+1)+1/(a+1)(a+2)+.+1/(a+2007)(a+2008)+1/(a+2011)(a+2012)
1/a(a+1)+1/(a+1)(a+2)+...+1/(a+2007)(a+2008)+1/(a+2011)(a+2012)
=1/a-1/(a+1)+1/(a+1)-1/(a+2)+...+1/(a+2007)-1/(a+2008)+1/(a+2011)-1/(a+2012)
=1/a-1/(a+2012)
=2012/[a(a+2012)]
