Question

1x4分之1十4x7分之1十7x11分之1十11x14分之1十14x17分之1等于几

Answer 1

1/(1*4)+1/(4*7)+1/(7*11)+1/(11*14)+1/(14*17)
=(1/3)*(1-1/4)+(1/3)*(1/4-1/7)+(1/4)*(1/7-1/11)+(1/3)*(1/11-1/14)+(1/3)*(1/14-1/17)

=(1/3)*(1-1/4+1/4-1/7)+(1/4)*(1/7-1/11)+(1/3)*(1/11-1/14+1/14-1/17)
=(1/3)*(1-1/7)+(1/4)*(1/7-1/11)+(1/3)*(1/11-1/17)
因为[(1/4)*(1/7-1/11)+(1/12)*(1/7-1/11)=(1/3)*(1/7-1/11)]
所以上式 =(1/3)*(1-1/7)+(1/3)*(1/7-1/11)+(1/3)*(1/11-1/17)-(1/12)*(1/7-1/11)
=(1/3)*(1-1/17)-(1/12)*(1/7-1/11)
=(1/12)*(1/4-1/68-1/7+1/11)
=(1/12)*(240/1309)
=20/1309
重要的是让你掌握方法，结果的话，有待于你再次验证一下！

该算式有一个规律：1/(a*b)=[1/(b-a)]*(1/a-1/b) ,你不妨验证一下！

Answer 2

算出来结果是16059/5236