Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. (If an answer does not exist, enter DNE.) 3 + 2.7 + 2.43 + 2.187 + ...

The series is convergent

Sum = 30

Step-by-step 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

a

step-by-step explanation: