Difference between revisions of "009C Sample Final 2, Problem 1"

Latest revision as of 18:20, 2 December 2017

Test if the following sequences converge or diverge. Also find the limit of each convergent sequence.

(a) $a_{n}={\frac {\ln(n)}{\ln(n+1)}}$

(b) $a_{n}={\bigg (}{\frac {n}{n+1}}{\bigg )}^{n}$

Solution

Detailed Solution

Return to Sample Exam

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 <span class="exam">Test if the following sequences converge or diverge. Also find the limit of each convergent sequence.
-<span class="exam">(a) &nbsp;<math style="vertical-align: -12px">a_n=\frac{\ln(n)}{\ln(n+1)}</math>
+<span class="exam">(a) &nbsp;<math style="vertical-align: -16px">a_n=\frac{\ln(n)}{\ln(n+1)}</math>
-<span class="exam">(b) &nbsp;<math style="vertical-align: -12px">a_n=\bigg(\frac{n}{n+1}\bigg)^n</math>
+<span class="exam">(b) &nbsp;<math style="vertical-align: -15px">a_n=\bigg(\frac{n}{n+1}\bigg)^n</math>
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+<hr>
-!Foundations: &nbsp;
+[[009C Sample Final 2, Problem 1 Solution|'''<u>Solution</u>''']]
-|-
-|'''L'Hopital's Rule'''
-|-
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-&nbsp; &nbsp; &nbsp; &nbsp; Suppose that <math>\lim_{x\rightarrow \infty} f(x)</math> &nbsp; and <math>\lim_{x\rightarrow \infty} g(x)</math> &nbsp; are both zero or both &nbsp; <math style="vertical-align: -1px">\pm \infty .</math>
-|-
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-&nbsp; &nbsp; &nbsp; &nbsp;If <math>\lim_{x\rightarrow \infty} \frac{f'(x)}{g'(x)}</math> &nbsp; is finite or &nbsp; <math style="vertical-align: -4px">\pm \infty ,</math>
-|-
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-&nbsp; &nbsp; &nbsp; &nbsp;then <math>\lim_{x\rightarrow \infty} \frac{f(x)}{g(x)}=\lim_{x\rightarrow \infty} \frac{f'(x)}{g'(x)}.</math>
-|}
-'''Solution:'''
-'''(a)'''
+[[009C Sample Final 2, Problem 1 Detailed Solution|'''<u>Detailed Solution</u>''']]
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Step 1: &nbsp;
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-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Step 2: &nbsp;
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-'''(b)'''
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Step 1: &nbsp;
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-!Step 2: &nbsp;
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-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Final Answer: &nbsp;
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-|&nbsp;&nbsp; '''(a)'''
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-|&nbsp;&nbsp; '''(b)'''
-|}
 [[009C_Sample_Final_2|'''<u>Return to Sample Exam</u>''']]

Difference between revisions of "009C Sample Final 2, Problem 1"

Latest revision as of 18:20, 2 December 2017

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