Question

2×1/3+3×1/4+4×1/5+5×1/6+6×1/7用简便方法算？

Answer 1

请听视频详细讲解方法。

Answer 2

=2/3+3/4+4/5+5/6+6/7
= （1+1+1+1+1）-（1/3+1/4+1/5+1/6+1/7）
= 5-[(1/3+1/4+1/6)+(1/5+1/7)]
= 5-[(4+3+2)/12+12/35]
= 5-[3/4+12/35]
=5-[1-1/4+12/35]
= 5-1-(12/35-1/4)
= 4-(48-35)/140
= 4-7/140
=4-1/20
= 3又19/20

Answer 3

2/3+3/4+4/5+5/6+6/7
=2/3+(1/4+2/4)+4/5+(2/6+3/6)+6/7
=2/3+1/2+1/4+4/5+1/3+1/2+6/7
=2/3+1/3+1/2+1/2+1/4+4/5+6/7
=1+1+1/4+4/5+6/7
=2+(5/20+16/20)+6/7
=2+[(20+1)/20]+6/7
=2+1+1/20+6/7
=3+(7/140+120/140)
=3+127/140
=3又127/140