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- Use the Test for Divergence to explain why if P∞ n=0 an converges, then P∞ n=0 1 an must diverge.Please comfirm if the following for D, E and F converges to a specific value or diverges.Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is inconclusive.∑n=1∞enn!ρ=limn→∞|an+1an|= (Enter 'inf' for ∞.) ∑n=1∞enn! is:A. convergentB. divergentC. The Ratio Test is inconclusive
- If a power series for some function y = g(x) has interval of convergence (−2, 2], is itpossible for the series for f′(x) to have interval of convergence [−2, 2]?Explain your answer.for what R is sigma n=1 (n!)^2/(K_n)! convergent?your work must clearly state which convergence test(s) you used, and evaluate the test(s) without skipping steps. NOTE: you can show decreasing by showing a derivative is negative. options a)converges conditionally b)converges absolutely c)diverges