前两项取1/3*1/5(1+1/7)
后面也是1/7*1/9(1/5+1/11)
第三个是1/11*1/13(1/9+1/15)
这样计吧
简便计算1\/1*3*5+1\/3*5*7+1\/5*7*9+1\/7*9*11+1\/9*11*13+1\/11*13*15...
=1\/4×(1\/1×3 -1\/3×5 +1\/3×5 -1\/5×7+...+1\/11×13 -1\/13×15)=1\/4×(1\/1×3 - 1\/13×15)=16\/195 结论:1\/n(n+1)(n+2)=1\/2×[1\/n(n+1) - 1\/(n+1)(n+2)]1\/n(n+2)(n+4)=1\/4×[1\/n(n+2) - 1\/(n+2)(n+4)]...
1\/1×3×5+1\/3×5×7+1\/5×7×9+1\/7×9×11+1\/9×11×13+1\/
分子和分母同时乘(1×3×5×7×9×11×13×15),然后再除这个数就可以了，把多次的除法变成多次乘法和仅仅一次的除法。
1\/1×3+1\/3×5+1\/5×7+1\/7×9+1\/9×11+1\/11×13的简便运算
=1\/1*3+1\/3*5+1\/5*7+1\/7*9+1\/9*11+1\/11*13 =1\/2*[(1-1\/3)+(1\/3-1\/5)+(1\/5-1\/7)+(1\/7-1\/9)+(1\/9-1\/11)+(1\/11-1\/13)} =1\/2*[1-1\/13]=6\/13
1\/(1×3×5) +1\/(3×5×7)+1\/(5×7×9)+…+1\/(11×13×15)这个式子怎么...
把通项1\/(a×b×c)改写成(1\/a-2\/b+1\/c)\/8,然后中间的项可以加减抵消掉，只需计算两端的若干个分数的运算即可。1\/(1×3×5) +1\/(3×5×7)+…+1\/(11×13×15)=(1\/1-2\/3+1\/5)\/8+(1\/3-2\/5+1\/7)\/8+...+(1\/11-2\/13+1\/15)\/8 =(1\/1-2\/3+1\/5+1\/3-2\/5+...
1\/3*5+1\/5*7+1\/7*9+1\/9*11+1\/11*13+1\/13*15=?
原式=1\/3*5+1\/5*7+1\/7*9+1\/9*11+1\/11*13+1\/13*15 =1\/2(1\/3-1\/5+1\/5-1\/7+...+1\/11-1\/13+1\/13-1\/15)=1\/2(1\/3-1\/15)=1\/2 * 4\/15 =2\/15 .
1\/1×3+1\/3×5+1\/5×7+1\/7×9+1\/9×11 = 多少?? 过程也写详细一点不要...
因为1\/1×3=1\/1-1\/3，所以以此类推，1\/(n-2)-1\/n=1\/(nx(n-2))，所以可得 1\/1×3＋1\/3×5+1\/5×7+1\/7×9+1\/9×11 =1\/1-1\/3+1\/3-1\/5+1\/5-1\/7+1\/7-1\/9+1\/9-1\/11=1\/1-1\/11=10\/11
1\/1×3×5+1\/3×5×7+1\/5×7×9×+……+1\/2001×2003×2005
1\/1×3×5=(1\\4)×(1\\(1×3)-1\\(3×5)) 就是将一乘三乘五分之一拆成一乘三分之一减去三乘五分之一后再乘四分之一 1\\3×5×7=(1\\4)×(1\\(3×5)-1\\(5×7))同理 ………1\\2001×2003×2005=(1\\4)×(1\\(2001×2003)-1\\(2003×2005))则原式=(1\\4)×(1\\(1×...
1\/1*3+1\/3*5+1\/5*7+1\/7*9+19*11+...+1\/1995*1997+1\/1997*1999的简便算 ...
1\/1*3=（1-1\/3）*0.5 1\/3*5=（1\/3-1\/5）*0.5 1\/5*7=（1\/5-1\/9）*0.5 1\/7*9=（1\/7-1\/9）*0.5 ...那么1\/1*3+1\/3*5+1\/5*7+1\/7*9+19*11+...+1\/1995*1997+1\/1997*1999 =（（1-1\/3）+（1\/3-1\/5）+（1\/5-1\/9）+...+（1\/1997-1\/1999））...
简便运算:1\/1*3+1\/3*5+1\/5*7+1\/7*9+1\/9*11
1\/1*3+1\/3*5+1\/5*7+1\/7*9+1\/9*11 =1\/2*（1-1\/3+1\/3-1\/5+1\/5-1\/7+1\/7-1\/9+1\/9-1\/11）=1\/2*（1-1\/11）=1\/2*10\/11 =5\/11
1\/(1*3*5)+1\/(3*5*7)+1\/(5*7*9)+1\/(7*9*11)
先通分,分母为1*3*5*7*9*11,第一式分子为7*9*11,第二式分子为1*9*11,第三式分子为1*3*11,第四式分子为1*3*5
