＝1/5－1/6+1/6－1/7+1/7－1/8+1/8－1/9+1/9－1/10
＝1/5－1/10
＝1/10
=1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
=1/5-1/10
=1/10本回答被网友采纳
1\/5×1\/6+1\/6×1\/7+1\/7×1\/8+1\/8×1\/9+1\/9×1\/10这道题用简便方法怎样做...
1\/6×1\/7=1\/6-1\/7,1\/7×1\/8=1\/7-1\/8,1\/8×1\/9=1\/8-1\/9 1\/9×1\/10=1\/9-1\/10 1\/5×1\/6＋1\/6×1\/7＋1\/7×1\/8＋1\/8×1\/9＋1\/9×1\/10 =1\/5-1\/6+1\/6-1\/7+1\/7-1\/8+1\/8-1\/9+1\/9-1\/10 =1\/5-1\/10 =2\/10-1\/10 =1\/10 类似的题有：写出...
1\/5×1\/6+1\/6×1\/7+1\/8×1\/9+1\/9×1\/10等于多少呢?求回答!
裂项法 1\/5×1\/6+1\/6×1\/7+1\/7×1\/8+1\/8×1\/9+1\/9×1\/10 =1\/5-1\/6+1\/6-1\/7+1\/7-1\/8+1\/8-1\/9+1\/9-1\/10 =1\/5-1\/10 =1\/10
1\/6×1\/7+1\/7×1\/8+1\/8×1\/9﹢1\/9×1\/10怎么算 要算式?
证明：(1\/a)*(1\/(a+1)=1\/a(a+1)=[(a+1)-a]\/a(a+1)=(a+1)\/a(a+1)-a\/a(a+1)=1\/\/a-1\/(a+1)所以：1\/6×1\/7+1\/7×1\/8+1\/8×1\/9+1\/9×1\/10 =1\/6-1\/7+1\/7-1\/8+1\/8-1\/9+1\/9-1\/10 =1\/6-1\/10 =1\/15 ...
怎样简算:1\/6×1\/7+1\/7×1\/8+1\/8×1\/9+1\/9×1\/10
如下：1\/6×1\/7+1\/7×1\/8+1\/8×1\/9+1\/9×1\/10 =1\/6-1\/7+1\/7-1\/8+1\/8-1\/9+1\/9-1\/10 =1\/6-1\/10 =5\/30-3\/30 =1\/15 除法的运算性质 1、被除数扩大（缩小）n倍，除数不变，商也相应的扩大（缩小）n倍。2、除数扩大（缩小）n倍，被除数不变，商相应的缩小（扩大）...
六分之一乘七分之一加七分之一乘八分之一加八分之一乘九分之一加九分...
1\/6×1\/7+1\/7×1\/8+1\/8×1\/9+1\/9×1\/10 =1\/6-1\/7+1\/7-1\/8+1\/8-1\/9+1\/9-1\/10 =1\/6-1\/10 =2\/30 =1\/15
1\/4*5*6 +1\/5*6*7 +1\/6*7*8+...+1\/98*99*100如何计算?
解析:=247\/9900.关键是要把1\/4*5*6这种等式拆成差式。我们知道，1\/n(n+1)=1\/n-1\/(n+1)，于是 1\/n(n+1)(n+2)=[1\/n-1\/(n+1)]*1\/(n+2)=1\/n(n+2)-1\/(n+1)*1\/(n+2)=1\/2*(1\/n-1\/(n+2))-[1\/(n+1)-1\/(n+2)]这样加起来，可以消去许多中间项，最后...
6分之1+7分之1+8分之1+9分之1+10分之1分之1的结果的整数部分是多少
(1\/10)*5<1\/6+1\/7+1\/8+1\/9+1\/10<(1\/6)*5 ==>1\/2<1\/6+1\/7+1\/8+1\/9+1\/10<5\/6 所以6分之1+7分之1+8分之1+9分之1+10分之1分之1大于>6\/5 并小于<2 所以其整数部分=1
...奥数 算式(1\/2+1\/3+1\/4+1\/5+1\/6+1\/7+1\/8+1\/9+1\/10+1\/11+1\/12+1\/...
1818\/是一个2位的循环，小数点后第2004位，2005位是81 2004\/13=154.153846153846是一个6位的循环，小数点后第2004位，2005位是61 42+66+81+61=250 所以算式（1\/2+1\/3+1\/4+1\/5+1\/6+1\/7+1\/8+1\/9+1\/10+1\/11+1\/12+1\/13）×2004计算结果的小数点后第2004位数字是5 ...
1\/4*5*6+1\/5*6*7+1\/6*7*8+1\/7*8*9+...1\/98*99*100
解：1\/(4×5×6)=1\/2[1\/(4×5)-1\/(5×6)]1\/(5×6×7)=1\/2[1\/(5×6)- 1\/(6×7 )]1\/(6×7×8)=1\/2[1\/(6×7)- 1\/(7×8)]………1\/(98×99×100)=1\/2[1\/(98×99)-1\/(99×100)]∴1\/(4×5×6)+ 1\/(5×6×7)+ 1\/(6×7×8)+…..+ 1\/(98...
1\/3×1\/4=1\/3-1\/4 1\/5×1\/6=1\/5-1\/6 1\/6×1\/7=1\/6-1\/7 找出他们的规律...
解：1\/7×1\/8＝1\/7－1\/8 1\/8×1\/9＝1\/8－1\/9 1\/9×1\/10＝1\/9－1\/10 ………一般规律：1\/n×1\/﹙n＋1﹚＝1\/n－1\/﹙n＋1﹚1\/12+1\/20+1\/30 ＝1\/3×1\/4＋1\/4×1\/5＋1\/5×1\/6 ＝1\/3－1\/4＋1\/4－1\/5＋1\/5－1\/6 ＝1\/3－1\/6 ＝1\/6....
