step 1 recall that for the series sum(n = 0 to infinity) a_n the ratio test looks at the limit lim(n to…

step 1 recall that for the series sum(n = 0 to infinity) a_n the ratio test looks at the limit lim(n to infinity) |(a_n + 1)/a_n|. the value of this limit can determine if the series absolutely converges, diverges, or the test can be inconclusive. we are given the series sum(n = 0 to infinity) n!/95^n. identify the following terms. a_n = a_n + 1 = submit skip (you cannot come back)

step 1 recall that for the series sum(n = 0 to infinity) a_n the ratio test looks at the limit lim(n to infinity) |(a_n + 1)/a_n|. the value of this limit can determine if the series absolutely converges, diverges, or the test can be inconclusive. we are given the series sum(n = 0 to infinity) n!/95^n. identify the following terms. a_n = a_n + 1 = submit skip (you cannot come back)

Answer

Explanation:

Step1: Identify (a_n)

Given the series (\sum_{n = 0}^{\infty}\frac{n!}{95^n}), by the general - form of a series (\sum_{n=0}^{\infty}a_n), we have (a_n=\frac{n!}{95^n}).

Step2: Identify (a_{n + 1})

Replace (n) with (n + 1) in the formula for (a_n). So (a_{n+1}=\frac{(n + 1)!}{95^{n+1}}).

Answer:

(a_n=\frac{n!}{95^n}), (a_{n + 1}=\frac{(n + 1)!}{95^{n+1}})