1乘3分之一加3乘5分之1加5乘7分之1..............具体的看补充. 简便算法

1111------+------+------+.............+----------------=__________1×33×55×72011×2013麻... 1 1 1 1
------ + ------ + ------ + .............+ ----------------=__________
1×3 3×5 5×7 2011×2013
麻烦讲清楚一点!!!! 在线等.
急!!!!!!!!!!!!!!!!!!!!!!!!!!
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Alice_Fun诗颖
2013-02-01
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先把原式拆开,拆成1*1/3+1/3*1/5++...+1/2011*1/2012.
1*1/3+1/3*1/5 提出一个1/5 得到1/3*(1+1/5) 即1/3*6/5
在用这个加上后面的1/5*1/7 提出一个1/5 得到1/5*(2+1/7) 即1/5*15/7
重复中找到规律
得出最后 =1/2011*(2009+1/2013)
好像错掉了,我算了10分钟啊!
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LINQIANG0301
2013-02-01
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这个啊~ 真的是相当的难啊。
唉,不好说啊。你要我怎么给你说呢?
简便方法呢?还是比较麻烦的死法?
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望月688
2013-02-01
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列项相消法可以求出来。
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匿名用户
2013-02-01
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追问
你刷屏??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
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大赉香
2013-02-01
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原式可以变为:1/2(1-1/3+1/3-1/5+1/5-1/7+1/7+...+1/2011-1/2013)
=1/2(1-1/2013)
=1/2*2012/2013
=1006/2013
如果对了,支持我一下。谢谢。
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