Final answer:
To determine whether the geometric series is convergent or divergent, we need to check the common ratio. In this case, the series is convergent with a sum of approximately 1.43.
Step-by-step explanation:
To determine whether the geometric series is convergent or divergent, we need to check the common ratio (r) of the series. In this case, the common ratio is 0.3 (each term is obtained by multiplying the previous term by 0.3).
If |r| < 1, then the series is convergent. If |r| ≥ 1, then the series is divergent.
In our case, |0.3| = 0.3 < 1, so the series is convergent.
To find the sum of a convergent geometric series, we can use the formula:
Sum = a / (1 - r),
where 'a' is the first term and 'r' is the common ratio.
In our case, a = 1 and r = 0.3:
Sum = 1 / (1 - 0.3) = 1 / 0.7 = 1.42857142857 (rounded to 11 decimal places).