Question

1/6+1/12+1/30+1/42+1/56

Answer 1

解:1/6+1/12+1/30+1/42+1/56=1/2-1/3+
1/3-1/码旦如4+1/5-1/6+1/6-1/7+1/7-1/8=1/2-
1/4+1/5-1/8=1/2-1/4-1/迟启迟启8+1/5=1/8+1/5=
13/40

Answer 2

1/6+1/12+1/30+1/42+1/56
=1/6+1/12+1/20+1/30+1/42+1/56-1/20
=1/(2×3)+1/(3×4)+1/(4×5)+1/(5×6)+
1/(6×7)+1/(7×8)-1/20
=(1/誉竖渣2-1/3)+(1/3-1/4)+(1/4-1/5)+
(1/5-1/纤芦6)+(1/6-1/7)+(1/7-1/8)-1/20
=1/2-1/3+1/3-1/庆悄4+1/4-1/5+1/5-1/6+
1/6-1/7+1/7-1/8-1/20
=1/2-1/8-1/20
=20/40-5/40-2/40
=15/40-2/40
=13/40

Answer 3

原式=（1/2-1/3）+（1/迟渣中3-1/4）码山+（1/5-1/6）+（1/6-1/7）+（1/7-1/梁配8）=1/2-1/4+1/5-1/8=0.325。

Answer 4

原式=1/2-1/3+1/3-1/4+1/5-1/6+1/6-1/7+1/7-1/8
=1/2-1/4+1/5-1/8
=4/清坦配8-2/8-1/8+1/信嫌5
=1/8+1/答指5
=5/40+8/40
=13/40

Answer 5

＝0.325