1/1*4+1/4*7+1/7*10+...+1/97*100答案=1/3*(1-1/4+1/4-1/7+1/7-1/10+...+1/97-1/100)=33/100答案前面的1/3怎么得来的不明白求详细讲解
问题描述：
1/1*4+1/4*7+1/7*10+...+1/97*100答案=1/3*(1-1/4+1/4-1/7+1/7-1/10+...+1/97-1/100)=33/100答案前面的1/3怎么得来的不明白求详细讲解
答
1/1*4+1/4*7+1/7*10+...+1/97*100
=3*(1/1*4+1/4*7+1/7*10+...+1/97*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答案前面的1/3怎么得来的为什么要先乘以3后面再除以3呢或者是乘以1/3呢，看不明白意思，我是小学生1/1*4+1/4*7+1/7*10+...+1/97*100=3*(1/1*4+1/4*7+1/7*10+...+1/97*100)÷3=(3/1*4+3/4*7+3/7*11+......+3/97*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 1/1*4+1/4*7+1/7*10=3*(1/1*4+1/4*7+1/7*10)÷3=(3/1*4+3/4*7+3/7*10)÷3=(1-1/4+1/4-1/7+1/7-1/10)÷3=(1-1/10)÷3=9/30=3/10先乘以3后面再除以3或者乘以1/3是为了运算简便