Question

Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. (If an answer does not exist, enter DNE.) 2 + 0.6 + 0.18 + 0.054 + ...

Answer 1

sum: 2 6/7

Explanation:

The first term is 2, and the common ratio is 0.6/2 = 0.3. This value is less than 1, so the series converges.

The sum is ...

S = a0/(1 -r) = 2/(1 -0.3) = 2/0.7

S = 2 6/7