计算1/6+1/12+1/20+1/30+1/42

1/6=1/<2*3>=1/2-1/3
1/12=...=1/3-1/4
1/20=1/4-1/5
.
.
.
所以相加得1/2-1/7=5/14

5/14

解：由题意得：
1/6+1/12+1/20+1/30+1/42
=2/12+1/12+3/60+2/60+1/42
=1/4+1/12+1/42
=21/84+7/84+2/84
=5/14

RT 原试= 1/2 *1/3 + 1/3 * 1/4 + 1/4 * 1/5 + 1/5 * 1/6 +1/6 * 1/7
= (1/2 - 1/3) + (1/3 - 1/4) + (1/4 -1/5) + (1/5 -1/6) + (1/6 - 1/7)
= 1/2 - 1/7 = 6/14 = 3/7

1/6+1/6*1/2+1/6*3/10+1/6*1/5+1/6*1/7=5/21