Question

tính nhanh : A = 1/3 + 1/9 + 1/27 + 1/81+.....+1/59049

 

Answer 1

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

Answer 2

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