Question

简便运算，急着求解

Answer 1

=1/4+1/3*（1/4-1/7）+1/3*（1/7-1/10）+。。。+1/3*（1/97-1/100）
=1/4+1/3*1/4-1/3*1/100
=1/3-1/3*1/100
=1/3*99/100
=33/100

Answer 2

解：可用列项法来。
原式=1/(1*4)+1/(4*7)+1/(7+10)+......+1/(97*100)
=(1-1/4)/3+(1/4-1/7)/3+(1/7-1/10)/3+......+(1/97-1/100)/3
=(1-1/4+1/4-1/7+1/7-1/10+......+1/97-1/100)/3
=(1-1/100)/3
=(99/100)/3
=33/100

Answer 3

左边先看成1-1/4+1/4-1/7+1/7-1/10+……+1/97-1/100
在除以3看下，自己琢磨下

诀窍1-1/4+1/4-1/7+1/7-1/10+……+1/97-1/100+……+1/(3*n-2)-1/(3*n+1) 都是3n，所以突破口就是3，同理最后要是10n，最后的突破口就是10

Answer 4

15273458245473247

Answer 5

=1/3*(1-1/4)+1/3*（1/4-1/7）+1/3*（1/7-1/10）+…。+1/3*（1/97-1/100）
=1/4+1/3*1/4-1/3*1/100
=1/3-1/3*1/100
=1/3*99/100
=33/100