Answer:
The series is convergent
Sum = 30
Explanation:
Given the geometric series 3 + 2.7 + 2.43 + 2.187 + ..., to determine whether the geometric series is convergent or divergent, we need to check the value of its common ratio. A geometric series is tested for convergence or divergence based on the value of its common ratio.
If |r|< 1, the series is convergent
if |r|≥ 1, the series is divergent.
r is the common ratio
From the series given, the common ratio r = 2.7/3 = 2.43/2.7 = 2.187/2.43 = 0.9
since r = 0.9 which is less than 1, then the series is convergent.
Since the geometric series is tending to infinity, we will use the formula for calculating the sum to infinity of a geometric series to find its sum.
S∞ = a/1-r
a is the first term = 3
r is the common ratio = 0.9
S∞ = 3/1-0.9
S∞ = 3/0.1
S∞ = 30
The sum of the geometric series is 30