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

Ta có:

\(a=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{n}=\frac{39}{40}\)

Coi n=a.(a+1)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{a.\left(a+1\right)}\)

Ta thấy: 

\(\frac{1}{1.2}=1-\frac{1}{2};\frac{1}{2.3}=\frac{1}{2}-\frac{1}{3};...\)

\(\Rightarrow a=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{a}-\frac{1}{a+1}\)

\(=1+\frac{-1}{2}+\frac{1}{2}+\frac{-1}{3}+\frac{1}{3}+...+\frac{-1}{a}+\frac{1}{a}-\frac{1}{a+1}\)

\(=1+\left(\frac{-1}{2}+\frac{1}{2}\right)+\left(\frac{-1}{3}+\frac{1}{3}\right)+...-\frac{1}{a+1}\)

\(=1+0+0+...+0-\frac{1}{a+1}\)

\(\Rightarrow1-\frac{1}{a+1}=\frac{39}{40}\)

\(\Rightarrow a+1=40\Rightarrow a=39\)

\(\Rightarrow n=39.40=1560\)

1560 do ban

1560 link nhé

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

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

1560 chuẩn 100%

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

a=1/2+1/6+1/12+1/20+1/30+1/n

a=1/1-1/2+1/2-...+1/a+1

a=1+1/a-1=39

=>a=40

vay n=39X40=1560

ai h minh h lai

1560 nha ban