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A=\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+.........+\frac{1}{n}=\frac{39}{40}\)
A=\(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+..........+\frac{1}{ax\left(a+1\right)}=\frac{39}{40}\)
A=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.......+\frac{1}{a}-\frac{1}{a+1}=\frac{39}{40}\)
A=\(1-\frac{1}{a+1}=\frac{39}{40}\)
\(\frac{1}{a+1}=1-\frac{39}{40}\)
\(\frac{1}{a+1}=\frac{1}{40}\)
a+1=40
a=40-1
a=39
n=39x40
n=1560
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A = 1/2+1/6+1/12+1/20+1/30+...+1/n = 1/1.2 + 1/2.3 +1/3.4 + 1/4.5 + 1/5.6 ......+1/a.b ( với a; b là hai số tự nhiên liên tiếp và a.b = n )
A = 1/2 + (1/2 -1/3) +( 1/3 -1/4) +(1/4 -1/5) +(1/5 -1/6) + ......
+( 1/a -1/b) = 1-1/b = 39/40 => b = 40 ; suy ra a = 39
vậy n = 39 x 40 =1560
A = 1/2+1/6+1/12+1/20+1/30+...+1/n = 1/1.2 + 1/2.3 +1/3.4 + 1/4.5 + 1/5.6 ......+1/a.b ( với a; b là hai số tự nhiên liên tiếp và a.b = n )
A = 1/2 + (1/2 -1/3) +( 1/3 -1/4) +(1/4 -1/5) +(1/5 -1/6) + ......
+( 1/a -1/b) = 1-1/b = 39/40 => b = 40 ; suy ra a = 39
vậy n = 39 x 40 =1560
![](https://rs.olm.vn/images/avt/0.png?1311)
1/2 + 1/6 + 1/12 + 1/20 + ... + 1/n = 39/40
1/(1x2) + 1/(2x3) + 1/(3x4) + 1/(4x5) + ... + 1/n = 39/40
1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... - 1/n = 39/40
1 - 1/n = 39/40
=> 1/n = 1 - 39/40 = 1/40
=> n = 40
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta thấy:
1/2 = 1/(1x2) = 1 - 1/2
1/6 = 1/(2x3) = 1/2 - 1/3
1/12 = 1/(3x4) = 1/3 - 1/4
........
Coi 1/n = 1/(ax(a+1)) = 1/a - 1/(a+1)
1 /2 + 1/6 + 1/12 + 1/20 + 1/30 +...+ 1/n = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +...+1/a - 1/(a+1) = 49/50
=1-1/2+1/2-1/3+1/3-......+1/a-1/a+1
Hay A = 1 - 1/(a+1) = 49/50
=> 1/(a+1) = 1 - 49/50
1/(a+1) = 1/50
Vậy (a + 1) = 50 mà n = a x (a+1) => n = (50-1) x 50 = 2450
Ta thấy:
1/2 = 1/(1x2) = 1 - 1/2
1/6 = 1/(2x3) = 1/2 - 1/3
1/12 = 1/(3x4) = 1/3 - 1/4
........
Coi 1/n = 1/(ax(a+1)) = 1/a - 1/(a+1)
1 /2 + 1/6 + 1/12 + 1/20 + 1/30 +...+ 1/n = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +...+1/a - 1/(a+1) = 49/50
=1-1/2+1/2-1/3+1/3-......+1/a-1/a+1
Hay A = 1 - 1/(a+1) = 49/50
=> 1/(a+1) = 1 - 49/50
1/(a+1) = 1/50
Vậy (a + 1) = 50 mà n = a x (a+1) => n = (50-1) x 50 = 2450
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)