Question

Use the Root Test to determine whether the series is convergent or divergent.

n=0∑[infinity] (arctann) n

Answer 1

The Root Test cannot be used to determine the convergence or divergence of the given series.

Step-by-step explanation:

The question asks us to use the Root Test to determine whether the series ∑(arctann) n=0∞ is convergent or divergent.

The Root Test states that if lim(n→∞) ((arctann)^(1/n)) = L, then the series is convergent if L < 1 and divergent if L > 1.

Let's calculate the limit of ((arctann)^(1/n)):

lim(n→∞) ((arctann)^(1/n)) = lim(n→∞) (arctann)^(1/n) = 1

Since the limit is equal to 1, we cannot determine whether the series is convergent or divergent using the Root Test. Therefore, we need to use a different convergence test to determine the convergence or divergence of this series.