Evaluate the series 6+2+2/3+2/9 + ... a6

The given above is a series that is geometric with the value of common ratio equal to 1/3. The sum of the first six terms of the sequence is,

S6 = a1 x (1 - r^6) / (1 - r)

Substituting the given,

S6 = 6 x (1 - (1/3) ^6) / (1 - 1/3)

The final value of the series is 728/81.