1*1⼀4+4*1⼀7+7*1⼀10+...+97*1⼀100简便方法计算

2024-12-24 17:54:00
推荐回答(2个)
回答1:

是1/(1×4)+1/(4×7)+1/(7×10)+...+1/(97×100)吧?
=(1-1/4+1/4-1/7+...+1/97-1/100)÷3
=(1-1/100)÷3
=99/100÷3
=33/100

回答2:

解:
1*1/4+4*1/7+7*1/10+...+97*1/100
=1/3*(1-1/4)+1/3*(1/4-1/7)+1/3*(1/7-1/10)+……+1/3*(1/97-1/100)
=1/3*[(1-1/4)+(1/4-1/7)+(1/7-1/10)+……+(1/97-1/100)]
=1/3*(1-1/100)
=1/3*99/100
=33/100