7/6+13/12+21/20+31/30+…+421/420
问题描述：
7/6+13/12+21/20+31/30+…+421/420
答
19又19/42
答
=(1+1/6)+(1+1/12)+(1+1/20)+(1+1/30)....+(1+1/420)
=(1+1/2-1/3)+(1+1/3-1/4)+(1+1/4-1/5)...(1+1/20-1/21)
=19+1/2-1/21=?
答
原式= 1 + 1/(2*3) + 1 +1/(3*4) + 1 +1/(4*5) + .+ 1 +1/(20*21)
=19 + (1/2 -1/3) + (1/3 -1/4) +（1/4 -1/5) + .+ (1/20 -1/21)
= 19 + 1/2 -1/21
=19又19/42
答
7/6+13/12+21/20+31/30+…+421/420
=1+1/6+1+1/12+1+1/20+....+1+1/420
=(1+1+1+。。。+1)+[1/(2*3)+1/(3*4)+1/(4*5)+....+1/(20*21)]
=19+(1/2-1/3+1/3-1/4+1/4-1/5+....+1/20-1/21)
=19+1/2-1/21
=19+19/42
=19又19/42