Show the convergence or divergence of the series, using the criteri...

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Show the convergence or divergence of the series, using the criterion of ratio. ∑_(n=1)^∞▒n!/(n-4)! Converges by the criterion of ratio Diverges by the criterion of ratio Criterion of ratio does not conclude/inconclusive Criterion of ratio does not apply Show the convergence or divergence of the series, using the criterion of the root. ∑_(n=1)^∞▒n^7/7^n Converges by the criterion of the root Diverges by the criterion of the root The root criterion does not conclude The root criterion does not apply Demonstrate the convergence and divergence of ∑_(n=1)^∞▒(-1)^(n+1)/n Diverges Converges conditionally Converges absolutely Cannot show convergence or divergence Use the test root to show whether the series ∑_(n=1)^∞▒(2n/(5n-1))^n converges or diverges Converges because lim┬(n→∞)⁡〖2n/(5n-1)〗=0 Diverges because lim┬(n→∞)⁡〖2n/(5n-1)〗=2/5 Converges because lim┬(n→∞)⁡〖2n/(5n-1)〗=2/5 The test is unfinished because lim┬(n→∞)⁡〖2n/(5n-1)〗=1 Determinar cuando la serie es absolutamente convergente, condicionalmente convergente o divergente. (Determine when the series is absolutely convergent, conditionally convergent or divergent.) ∑_(n=1)^∞▒(-1)^(n+1)/〖2n〗^2   ∑_(n=1)^∞▒(-1)^n/√(5&n)   ∑_(n=1)^∞▒(〖4n〗^2+3n+2)/(〖2n〗^2+n+1) Classify the serie like absolutely convergent or conditionally convergent a)diverges b)conditionally converges c)absolutely converges d)none   Investigate the convergence or divergence of the serie a)diverges by the integral criteria b)converges by the alternating series criteria c)diverges by the nth term criteria d)converges by the ratio criteria   Determine which of the following criteria should be used to demonstrate the convergence of the serie a)Root criteria b)Ratio criteria c)alternating series criteria d)geometric series criteria   Determine which of the following series converges   If the serie {} is conditionally convergent, determine which of the following series is divergent.   Investigate the convergence or divergence of the serie a)converges by the ratio criteria b)diverges by the root criteria c)converges by the geometric series criteria d)diverges by the geometric series criteria   Classify the serie like absolutely convergent or conditionally convergent a)diverges b)conditionally converges c)absolutely converges d)none

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