求解题过程,懂的不懂的都来看看答案怎么得来的1/3+1/15+1/35+1/63+1/99=1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11)=(1-1/11)x(1/2)=5/11知道过程的请说明第2步怎么得来的,要过程,谢谢!
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求解题过程,懂的不懂的都来看看答案怎么得来的1/3+1/15+1/35+1/63+1/99=1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11)=(1-1/11)x(1/2)=5/11知道过程的请说明第2步怎么得来的,要过程,谢谢!
求解题过程,懂的不懂的都来看看答案怎么得来的
1/3+1/15+1/35+1/63+1/99
=1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11)
=(1-1/11)x(1/2)
=5/11
知道过程的请说明第2步怎么得来的,要过程,谢谢!
求解题过程,懂的不懂的都来看看答案怎么得来的1/3+1/15+1/35+1/63+1/99=1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11)=(1-1/11)x(1/2)=5/11知道过程的请说明第2步怎么得来的,要过程,谢谢!
1/(1x3)=(1/1-1/3)/2
1/(3x5)=(1/3-1/5)/2
…………
原式等于＝(1/1-1/3+1/3-1/5+1/5-1/7+……+1/9-1/11)/2
中间项约掉得：=(1/1-1/11)/2
1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11)拆分 0.5*(1-1/3+1/3-1/5+1/5..... )相消
1/3+1/15+1/35+1/63+1/99
=1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11)
=1/2*[2/(1*3)+2/(3*5) +2/(5*7) +2/(7*9) +2/(9*11)]
=1/2*[(1-1/3)+(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)]
=(1-1/11)x(1/2)
=5/11
这种方法是裂项相消
/3+1/15+1/35+1/63+1/99
=1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11)
=1/2*[2/(1*3)+2/(3*5) +2/(5*7) +2/(7*9) +2/(9*11)]
=1/2*[(1-1/3)+(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)]
=(1-1/11)x(1/2)
=5/11
1/3+1/15+1/35+1/63+1/99
=1/(1*3)+1/(3*5)+1/(5*7)+1/(7*9)+1/(9*11)
=[1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11]/2
=(1-1/11)/2
=(10/11)/2
=5/11
1/3=1/2(1-1/3)
1/15=1/2(1/3-1/5)
1/35=1/2(1/5-1/7)
1/63=1/2(1/7-1/9)
1/99=1/2(1/9-1/11)
提取1/2就OK了
很简单，就是把分母拆开，3拆为1*3，15拆为3*5，。。。。
而再由于：1/(1x3)=(1/1-1/3)/2；
1/(3x5)=(1/3-1/5)/2；
。。。。。。
于是原式等于＝(1/1-1/3+1/3-1/5+1/5-1/7+……+1/9-1/11)/2
则得到结果=5/11
1/(1x3)=(1/2)x(1-1/(1x3))
后面同理
那就自然到了第三步