Question

1/6+1/12+1/20+1/30+1/42怎样算更简便。

Answer 1

1/2+1/6+1/12+1/20+1/30+1/42
=（1-1/2）+（1/2-1/3）+（1/3-1/4）+（1/4-1/5）+（1/5-1/6）+（1/6-1/7）
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1-（1/2-1/2）-（1/3-1/3）-（1/4-1/4）-（1/5-1/5）-（1/6-1/6）-1/7
=1-0-0-0-0-0-1/7
=6/7

Answer 2

1/6 = 70/420
1/12 = 35/420
1/20 = 21/420
1/30 = 14/420
1/42 = 10/420
总和 = 70/420 + 35/420 + 21/420 + 14/420 + 10/420
= 150/420
150/420 = 5/14
因此，1/6+1/12+1/20+1/30+1/42 的和是 5/14

Answer 3

解：原式＝1／4＋5／60＋1／42＝1／3＋1／42
＝（14＋1）／42＝15／42

Answer 4

1/6+1/12+1/20+1/30+1/42
=1/6+1/12+5/60+1/42
=1/6+2/12+1/42
=2/6+1/42
=15/42
=5/14

Answer 5

1/6+1/12+1/20+1/30+1/42
=2/12+1/12+（3/60+2/60）+1/42
=3/12+5/60+1/42
=3/12+1/12+1/42
=4/12+1/42
=1/3+1/42
=14/42+1/42
=15/42
=5/14