Final answer:
The general term of the series is n/3^(n-1) and the sum of n terms is 1(1 - (1/3)^n) / (1 - 1/3).
Step-by-step explanation:
The given series is 1 + 2/3 + 3/3² + 4/3³ + ...
To find the general term of this series, we can observe that each term in the numerator is the natural number itself, while each term in the denominator is a power of 3 starting from 3^1. So, the general term can be written as n/3^(n-1).
To find the sum of n terms of the series, we can use the formula for the sum of a geometric series: S_n = a(1 - r^n) / (1 - r), where a is the first term and r is the common ratio.
In this case, the first term is 1 and the common ratio is 1/3. Therefore, the sum of n terms is given by S_n = 1(1 - (1/3)^n) / (1 - 1/3).