Use the Ratio test to determine if the following series converges or diverges. \[ \sum_{n=7}^{\infty} \frac{n !(n+4) !}{(2 n) !} \] (a) Find \( a_{n+1}= \) (b) Find and simplify completely. Do not leave absolute values in your answer. \[ \left|\frac{a_{n+1}}{a_{n}}\right|= \] (c) Find \( L=\lim _{n \rightarrow \infty}\left|\frac{a_{n+1}}{a_{n}}\right|= \) (d) State a conclusion about the infinite series. The limit \( L \) is -- Select-- \( \hat{\nabla} \). The Ratio Test tells us ---Select---
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To do this, we replace \(n\) with \(n+1\) in the given formula for \(a_n\): \[a_{n+1} = \frac{(n+1)!(n+5)!}{(2(n+1))!}\] Show more…
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