Question

经典小学数学问题．．数学高手进

1／1×1／4＋1／4×1／7＋1／7×1／10＋1／10×1／13＋．．．．．．．1／94×1／97＋1／97×1／100
谁能做出来．．快快地．．．要用小学的简便方法做．详细点．．．．

Answer 1

1-1/4=3/4
1/4-1/7=3/28
1/7-1/10=3/70
......
1/97-1/100=3/9700.
等号左右两边分别相加得：
1-1/4+1/4-1/7+......+1/97-1/100=1-1/100=99/100
=3*(1/4+1/28+1/70+......+1/9700)
=3*（1/1*1/4+1/4*1/7+1/7*1/10+......+1/97*1/100)
=99/100

所以原式1／1×1／4＋1／4×1／7＋1／7×1／10＋1／10×1／13＋．．．．．．．1／94×1／97＋1／97×1／100
=33/100

Answer 2

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

请给分

Answer 3

=33/100

Answer 4

=1/3[(1-1/4)+(1/4-1/7)+...+(1/97-1/100)]
=1/3*(1-1/100)
=33/100

Answer 5

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

Answer 6

1／1×1／4＋1／4×1／7＋1／7×1／10＋1／10×1／13＋．．．．．．．1／94×1／97＋1／97×1／100
=1/3×(1/1-1/4)+1/3×(1/4-1/7)+...1/3×(1/97-1/100)
=1/3×(1-1/4+1/4-1/7+1/7...-1/100)
=1/3×99/100
=33/100
=0.33