Question

Test the series for convergence or divergence.\\ $\sum_{n=1}^{\infty} \frac{(n+7)7^n}{5^{2n+3}}$.\\ Use the Ratio Test and evaluate:\\ $\lim_{n\to\infty} \frac{7(n+8)}{5(n+7)} = \frac{7}{5}$ \\ (Note: Use INF for an infinite limit.)\\ Since the limit is finite the series diverges

          Test the series for convergence or divergence.\\
$\sum_{n=1}^{\infty} \frac{(n+7)7^n}{5^{2n+3}}$.\\
Use the Ratio Test and evaluate:\\
$\lim_{n\to\infty} \frac{7(n+8)}{5(n+7)} = \frac{7}{5}$ \\
(Note: Use INF for an infinite limit.)\\
Since the limit is finite the series diverges

Test the series for convergence or divergence.

∑n=1^∞((n+7)7^n)/(5^2n+3).

Use the Ratio Test and evaluate:

limn→∞(7(n+8))/(5(n+7)) = (7)/(5)

(Note: Use INF for an infinite limit.)

Since the limit is finite the series diverges

Added by Pamela J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

08/01/2023

Step 1

The Ratio Test states that for a series \sum a_n, if lim |a_(n+1)/a_n| as n approaches infinity is L, then: - If L < 1, the series converges absolutely. - If L > 1 or L = ∞, the series diverges. - If L = 1, the test is inconclusive. In this case, we have: a_n = Show more…

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Test the series for convergence or divergence. sum_(n=1)^(infty ) ((n+7)7^(n))/(5^(2n+3)) Use the and evaluate: lim_(n->infty )(7(n+8))/(5(n+7)) (Note: Use INF for an infinite limit.) Since the limit is the series diverges Test the series for convergence or divergence uL(L+u) v 52n+3 Use the Ratio Test and evaluate lim 7n+8/5n+7 n (Note: Use INF for an infinite limit.) /5 Since the limit is finite the series diverges