determine whether the geometric series is convergent or divergent. if it is convergent, find the sum.\n5 - 6…

determine whether the geometric series is convergent or divergent. if it is convergent, find the sum.\n5 - 6 + \\frac{36}{5} - \\frac{216}{25} + \\cdots

determine whether the geometric series is convergent or divergent. if it is convergent, find the sum.\n5 - 6 + \\frac{36}{5} - \\frac{216}{25} + \\cdots

Answer

Explanation:

Step1: Identify the first - term and common ratio

The first - term (a = 5). The common ratio (r=\frac{-6}{5}=- \frac{6}{5}).

Step2: Check the convergence condition

For a geometric series (\sum_{n = 0}^{\infty}ar^{n}), it converges if (|r|\lt1) and diverges if (|r|\geq1). Here, (|r|=\left|-\frac{6}{5}\right|=\frac{6}{5}\gt1).

Answer:

The geometric series is divergent.