搜搜考试网1/1*4+1/4*7+1/7*10+...+1/97*100答案=1/3*(1-1/4+1/4-1/7+1/7-1/1
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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
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
再问： 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
再答： 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 =(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
=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
再问： 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
再答： 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 =(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