Question

Test the series for convergence or divergence.\\ Use the Ratio Test and evaluate: \\ $\lim_{n \to \infty}$ \\ Since the limit is greater than 1, the series diverges\\ $\sum_{n=1}^{\infty} \frac{10^n}{(n+7)^2 \cdot 8^{n+2}} = \frac{10}{8}$ (Note: Use INF for an infinite limit.)

          Test the series for convergence or divergence.\\
Use the Ratio Test and evaluate: \\
$\lim_{n \to \infty}$ \\
Since the limit is greater than 1, the series diverges\\
$\sum_{n=1}^{\infty} \frac{10^n}{(n+7)^2 \cdot 8^{n+2}} = \frac{10}{8}$ (Note: Use INF for an infinite limit.)

Test the series for convergence or divergence.

Use the Ratio Test and evaluate:

limn →∞

Since the limit is greater than 1, the series diverges

∑n=1^∞(10^n)/((n+7)^2 · 8^n+2) = (10)/(8) (Note: Use INF for an infinite limit.)

Added by Michael A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

01/09/2024

Step 1

Step 1: The Ratio Test states that if $$\lim_{n \to \infty} \left| \frac{a_{n+1}}{a_n} \right| = L$$, then the series converges if $L < 1$, diverges if $L > 1$, and the test is inconclusive if $L = 1$. Show more…

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Test the series for convergence or divergence. $$\sum_{n=1}^{\infty} \frac{10^n}{(n+7)^2 \cdot 8^{n+2}}$$ Use the Ratio Test and evaluate: $$\lim_{n \to \infty} $$ Since the limit is greater than 1 the series diverges = 10/8 (Note: Use INF for an infinite limit.)