Question

Use the ratio test to determine whether the series is convergent or divergent. ∞ 2 · 4 · 6 · · (2n) n! n = 1

Answer 1

The given series is divergent according to the ratio test.

Step-by-step explanation:

The given series is ∞ 2 · 4 · 6 · · (2n) / n!. To determine whether this series is convergent or divergent, we can use the ratio test.

The ratio test states that if the limit of the absolute value of the ratio between consecutive terms is less than 1, the series is convergent. If the limit is greater than 1, the series is divergent.

Let's apply the ratio test to this series:

lim┬(n→∞)⁡〖(a_(n+1) / a_n)〗 = lim┬(n→∞)⁡(2(2n + 2) / (n + 1)(2n)) = 2

Since the limit is greater than 1, the series is divergent.

Answer 2

A group of environmentalists were discussing the benefits and drawbacks associated with using fossil fuels. Which argument best fits the conversation?
Fossil fuels are cheaper than alternative forms of energy.Fossil fuel reserves will never be depleted.Fossil fuels are easily renewed. Fossil fuel use does not affect the environment.