3M = 3(5/3+8/3^2+11/3^3+...+302/3^100) = 5 + 8/3 + 11/3^2 + ... + 302/3^99

3M - M = ( 5 + 8/3 + 11/3^2 + ... + 302/3^99 ) - ( 5/3+8/3^2+11/3^3+...+302/3^100 ) 

2M = 5 + 8/3 + 11/3^2 + ... + 302/3^99 - 5/3 - 8/3^2 - 11/3^3 - ... - 302/3^100

2M = 5 + 1 + 1/3 + 1/3^2 + ... + 1/3^98 - 302/3^100                  (1)

Đặt B = 1/3 + 1/3^2 + 1/3^3 + ... + 1/3^98

3B = 1 + 1/3 + 1/3^2 + ... + 1/3^97

3B - B = 1 + 1/3 + 1/3^2 + ... + 1/3^97 - 1/3 - 1/3^2 - 1/3^3 - ... - 1/3^98

2B = 1 - 1/3^98

B = 1/2 - 1/3^98         (2)

Từ (1) và (2) => 2G = 5 + 1 + 1/3 + 1/3^2 + ... + 1/3^98 - 302/3^100 = 6 + 1/2 - 1/3^98

=> G = 3 + 1/4 - 1/3^98

ta có 0 < 1/4 - 1/3^98 < 1/2

=> 3 < 3 + 1/4 - 1/3^98 < 3 + 1/2      

suy ra 2 + 5/9 < G < 3 + 1/2