Question

Use the Ratio Test to determine the convergence or divergence of the series. (If you need to use ? or -?, enter INFINITY or -INFINITY, respectively.) ?_{n=1}^{?} 2/n! lim_{n??} |a_{n+1}/a_{n}| = 2 converges diverges inconclusive

          Use the Ratio Test to determine the convergence or divergence of the series. (If you need to use ? or -?, enter INFINITY or -INFINITY, respectively.)
?_{n=1}^{?} 2/n!
lim_{n??} |a_{n+1}/a_{n}| = 2
converges
diverges
inconclusive

Added by Ann A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ben Blakesley

07/25/2022

Step 1

Step 1:** Calculate the ratio of consecutive terms: \[ \frac{a_{n+1}}{a_n} = \frac{\frac{2}{(n+1)!}}{\frac{2}{n!}} = \frac{2}{(n+1)!} \times \frac{n!}{2} = \frac{1}{n+1} \] ** Show more…

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Use the Ratio Test to determine the convergence or divergence of the series. (If you need to use ∞ or -∞, enter INFINITY or -INFINITY, respectively.) ∑_{n=1}^{∞} 2/n! lim_{n→∞} |a_{n+1}/a_{n}| = converges diverges inconclusive