(1/2)+(1/6)+(1/12)+(1/20)+(1/30)+.+(1/420)

来源：学生作业帮助网编辑：作业帮时间：2024/04/29 18:16:47

(1/2)+(1/6)+(1/12)+(1/20)+(1/30)+.+(1/420)
(1/2)+(1/6)+(1/12)+(1/20)+(1/30)+.+(1/420)

(1/2)+(1/6)+(1/12)+(1/20)+(1/30)+.+(1/420)
(1/2)+(1/6)+(1/12)+(1/20)+(1/30)+.+(1/42)
=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

(1/2)+(1/6)+(1/12)+(1/20)+(1/30)+......+(1/420)
=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+......+1/(20*21)
=1-1/2+1/2-1/3+1/3-1/4+1/4-15+1/5-1/6+....+1/20-1/21
=1-1/21
=20/21

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(1/2)+(1/6)+(1/12)+(1/20)+(1/30)+......+(1/420)
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+......+(1/20-1/21)
=1-1/21
=20/21

原式=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+···+1/20-1/21
=1-1/21
=20/21

可以简算，化为：1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+......+1/60-1/70=1-1/70=69/70

解由1/2=1-1/2
1/6=1/2-1/3
1/12=1/3-1/4
1/20=1/4-1/5
1/30=1/5-1/6
...............................
1/380=1/19-1/20
1/420=1/20-1/21
即(1/2)+(1/6)+(1/12)+(1/20)+(1/30)+......+(1/420)
=（1-1/2）+（1/2-1/3）+（1/3-1/4）+.....+(1/19-1/20)+(1/20-1/21)
=1-1/21
=20/21

(1/2)+(1/6)+(1/12)+(1/20)+(1/30)+......+(1/420)
=1/2+1/（2×3）+1/（3×4）+1/（4×5）+......+1/(20×21)
=1/2+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+.....+(1/20-1/21)
=1-1/21
=20/21

(1/2)+(1/6)+(1/12)+(1/20)+(1/30)+......+(1/420)
=1/（1×2）+1/（2×3）+1/（3×4）+……+1/（20×21）
=（1/1-1/2）+（1/2-1/3）+（1/3-1/4）+……+（1/20-1/21）
=1-（1/2-1/2）-（1/3-1/3）-……-（1/20=1/20）-1/21
=1-1/21
=20/21

1/2+1/6+1/12+1/20.+1/380 2%1+6%1+12%1+20%1+30%1 1/2+1/6+1/12+1/20+1/30 1/2-1/6-1/12-1/20-...-1/110 1/2,-1/6,1/12,-1/20,1/30 2/1+6/1+12/1+24/1+48/1 1/2+1/6+1/12+1/20+.1/90 2/1+6/1+12/1+20/1+...+2450/1 1/2+1/6+1/12+...+1/4054182 等于多少? 1/2+1/6+1/12+...+1/56=快 1/2+1/6+1/12+1/20= 1/2+1/6+1/12+.1/9900 1/2+1/6+1/12+.+1/9900 1/2+1/6+1/12+...+1/72简便运算计算1/2+1/6+1/12+1/20.1/90 1/2+1/6+1/12+1/20（简算） 1/2+1/6+1/12+1/20的数列 2/1+6/1+12/1+.+4038090/1等于多少?