A=1/3+1/9+1/27+1/81+......+1/95049

Ax3=3x(1/3+1/9+1/27+1/81+.........+1/95049)

Ax3=1+1/3+1/9+1/27+1/81+..........+1/19683

Ax3-A=1+1/3+1/9+1/27+1/81+............+1/19683

- (1+1/3+1/9+1/27+1/81+........+1/59049)

=1-1/59049

2xA=59048/59049

A=59048/59049:2

A=29524/59049

giúp với help me

mình ko biết làm

I = 1 + 3^1 + 3^2 + ...+3^10

3I = 3^1 + 3^2 + ... + 3^11

3I - I = 3^1 + 3^2 + ... + 3^11 - 1 - 3^1 - 3^2 - ... - 3^10

 2I      = 3^11 - 1

I         = \(\frac{3^{11}-1}{2}=\frac{177147-1}{2}=\frac{177146}{2}=88573\)

A = 1/3 + 1/9 + 1/27 + 1/81 + ... + 1/59049

3 x A = 3 x ( 1/3 + 1/9 + 1/27 + 1/81 + ... + 1/59049 )

3 x A = 1 + 1/3 + 1/9 + 1/27 + 1/81 + ... + 1/19683 

3 x A - A = 1 + 1/3 + 1/9 + 1/27 + 1/81 + ... + 1/19683 

- ( 1 + 1/3 + 1/9 + 1/27 + 1/81 + ... + 1/59049 )

= 1 - 1/59049 

2 x A = 59048/59049

A = 59048/59049 : 2

A = 29524/59049

A = 1/3 + 1/9 + 1/27 + 1/81 + ... + 1/59049

3 x A = 3 x ( 1/3 + 1/9 + 1/27 + 1/81 + ... + 1/59049 )

3 x A = 1 + 1/3 + 1/9 + 1/27 + 1/81 + ... + 1/19683 

3 x A - A = 1 + 1/3 + 1/9 + 1/27 + 1/81 + ... + 1/19683 - ( 1 + 1/3 + 1/9 + 1/27 + 1/81 + ... + 1/59049 )

= 1 - 1/59049 

2 x A = 59048/59049

A = 59048/59049 : 2

A = 29524/59049

A = 1/3 + 1/9 + 1/27 + 1/81 + ... + 1/59049

3 x A = 3 x ( 1/3 + 1/9 + 1/27 + 1/81 + ... + 1/59049 )

3 x A = 1 + 1/3 + 1/9 + 1/27 + 1/81 + ... + 1/19683

3 x A - A = 1 + 1/3 + 1/9 + 1/27 + 1/81 + ... + 1/19683

- ( 1 + 1/3 + 1/9 + 1/27 + 1/81 + ... + 1/59049 )

= 1 - 1/59049

2 x A = 59048/59049

A = 59048/59049 : 2

A = 29524/59049

ta có :

= ( 1 + 59049 ) + ( 3 + 2187 ) + ( 9 + 6561 ) + ( 27 + 243 ) + ( 81 + 729 )

= 59050 + 2190 + 6570 + 270 + 810

= 59050 + ( 2190 + 810 ) + 6570 + 270

= 59050 + 3000 + 6570 + 270

= 59050 + ( 3000 + 6570 ) + 270

= 59050 + 9570 + 270

= 68620 + 270

= 68890

68890

Kết quả là 68890

Nhớ trả lời cho mình

 Đặt   \(A=\frac{1}{3}+\frac{1}{9}+.......+\frac{1}{59049}\)

  \(3A=3.\left(\frac{1}{3}+\frac{1}{9}+......+\frac{1}{59049}\right)\)

\(3A=1+\frac{1}{3}+........+\frac{1}{19683}\)

\(3A-A=\left(1+\frac{1}{3}+......+\frac{1}{19683}\right)-\left(\frac{1}{3}+\frac{1}{9}+........+\frac{1}{59049}\right)\)

\(2A=1-\frac{1}{59049}\)

\(2A=\frac{59048}{59049}\)

\(A=\frac{59048}{59049}:2\)

\(A=\frac{59048}{118098}\)