Question

Test the series for convergence or divergence. ?_{n=1}^? (3^n n!) / (13 ? 18 ? 23 ??? (5n + 8)). Use the Ratio Test and evaluate: lim_{n ? ?} = 1/5 . (Note: Use INF for an infinite limit.) Since the limit is less than 1, the series converges absolutely.

          Test the series for convergence or divergence.
?_{n=1}^? (3^n n!) / (13 ? 18 ? 23 ??? (5n + 8)).
Use the Ratio Test and evaluate:
lim_{n ? ?} = 1/5 . (Note: Use INF for an infinite limit.)
Since the limit is less than 1, the series converges absolutely.

Test the series for convergence or divergence.
?n=1^? (3^n n!) / (13 ? 18 ? 23 ??? (5n + 8)).
Use the Ratio Test and evaluate:
limn ? ? = 1/5 . (Note: Use INF for an infinite limit.)
Since the limit is less than 1, the series converges absolutely.

Added by Rodney L.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

08/01/2023

Step 1

We can see that the terms in the sequence Sn are of the form 13 + 5n, so we can write: Sn+9 = 13 + 5(n+2) Sn+8 = 13 + 5(n+1) Substituting these expressions into the limit, we get: lim n→∞ (13 + 5(n+2))/(13 + 5(n+1)) = lim n→∞ (13 + 5n + 10)/(13 + 5n + 5) = Show more…

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Test the series for convergence or divergence: ̑̄ ∑(n=1 to ∞) (3^n n!) / (13 * 18 * 23 * ... * (5n + 8)) Use the Ratio Test and evaluate: lim (n → ∞) = 1/5. (Note: Use INF for an infinite limit.) Since the limit is less than 1, the series converges absolutely.