Question

1/2加1/6加1/12加1/20加1/30加1/42简便运算

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
=1-1/7
=6/7

Answer 2

1/2+1/6+1/12+1/20+1/30+1/42
=1/2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7
=1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1/2-1/7
=(7-2)/14
=5/14