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Consider the following series. \sum_{n=1}^{\infty} \frac{n^{k-1}}{n^k+3} \quad k>2 Use the Limit Comparison Test to complete the limit. \lim_{n \to \infty} \frac{n^{k-1}}{n^k+3} \quad \to L>0 Determine the convergence or divergence of the series. \circ converges \circ diverges Need Help? Read It Watch It Master It 8. [0.5/1 Points] DETAILS PREVIOUS ANSWERS LARCALC12 9.4.026. Consider the following series. \sum_{n=1}^{\infty} \sin(\frac{1}{n}) Use the Limit Comparison Test to complete the limit. \lim_{n \to \infty} \frac{\sin(\frac{1}{n})}{\frac{1}{n}} \quad \to L>0 Determine the convergence or divergence of the series. \circ converges \circ diverges Need Help? Read It Watch It

          Consider the following series.
\sum_{n=1}^{\infty} \frac{n^{k-1}}{n^k+3} \quad k>2
Use the Limit Comparison Test to complete the limit.
\lim_{n \to \infty} \frac{n^{k-1}}{n^k+3} \quad \to L>0
Determine the convergence or divergence of the series.
\circ converges
\circ diverges
Need Help?
Read It
Watch It
Master It
8. [0.5/1 Points]
DETAILS
PREVIOUS ANSWERS
LARCALC12 9.4.026.
Consider the following series.
\sum_{n=1}^{\infty} \sin(\frac{1}{n})
Use the Limit Comparison Test to complete the limit.
\lim_{n \to \infty} \frac{\sin(\frac{1}{n})}{\frac{1}{n}} \quad \to L>0
Determine the convergence or divergence of the series.
\circ converges
\circ diverges
Need Help?
Read It
Watch It
        
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Consider the following series.
∑n=1^∞ (n^k-1)/(n^k+3)   k>2
Use the Limit Comparison Test to complete the limit.
limn →∞ (n^k-1)/(n^k+3)   →L>0
Determine the convergence or divergence of the series.
∘converges
∘diverges
Need Help?
Read It
Watch It
Master It
8. [0.5/1 Points]
DETAILS
PREVIOUS ANSWERS
LARCALC12 9.4.026.
Consider the following series.
∑n=1^∞ sin((1)/(n))
Use the Limit Comparison Test to complete the limit.
limn →∞ (sin((1)/(n)))/((1)/(n))   →L>0
Determine the convergence or divergence of the series.
∘converges
∘diverges
Need Help?
Read It
Watch It

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Consider the following series. Use the Limit Comparison Test to complete the limit: lim (k+3)/(k-1) as k approaches 0. Determine the convergence or divergence of the series: Converges or Diverges. Need Help? Rod Watchster.
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Transcript

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00:01 So here we just have to look at the what does 1 over root n look like? square root of n squared plus 7.
00:12 Well the easiest thing to check is well as n goes to infinity this basically looks like 1 over square root of n because 7 is very small compared to infinity and 1 over square root of n, 1 over square root of n squared i mean, 1 over square root of n squared is just 1 over n.
00:32 So let's look at this limit, the limit as n goes to infinity of this.
00:40 Well this would be n over square root of n squared plus 7 limit.
00:55 Okay and now what is the limit of this? well as i said before since we're going to infinity the 7 basically doesn't matter...
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