009C Sample Final 3, Problem 3 - Revision history

Kayla Murray at 01:43, 3 December 2017

2017-12-03T01:43:48Z

2017-03-17T18:03:36Z

2017-03-05T22:48:20Z

2017-03-05T22:43:59Z

2017-03-05T00:53:46Z

2017-02-18T18:44:35Z

@@ Line 3: / Line 3: @@
 ::<math>\sum_{n=1}^{\infty} \frac{n^3+7n}{\sqrt{1+n^{10}}}</math>
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+<hr>
-!Foundations: &nbsp;
+[[009C Sample Final 3, Problem 3 Solution|'''<u>Solution</u>''']]
-'''Solution:'''
+[[009C Sample Final 3, Problem 3 Detailed Solution|'''<u>Detailed Solution</u>''']]
 [[009C_Sample_Final_3|'''<u>Return to Sample Exam</u>''']]

@@ Line 76: / Line 76: @@
 !Final Answer: &nbsp;
 |-
-|&nbsp; &nbsp; &nbsp; &nbsp; converges
+|&nbsp; &nbsp; &nbsp; &nbsp; converges (by the Limit Comparison Test)
 |}
 [[009C_Sample_Final_3|'''<u>Return to Sample Exam</u>''']]

@@ Line 10: / Line 10: @@
 |&nbsp; &nbsp; &nbsp; &nbsp; Let &nbsp;<math>\{a_n\}</math>&nbsp; and &nbsp;<math>\{b_n\}</math>&nbsp; be positive sequences.
 |-
-|&nbsp; &nbsp; &nbsp; &nbsp; If &nbsp;<math>\lim_{n\rightarrow \infty} \frac{a_n}{b_n}=L,</math>&nbsp; where &nbsp;<math>L</math> &nbsp; is a positive real number,
+|&nbsp; &nbsp; &nbsp; &nbsp; If &nbsp;<math style="vertical-align: -16px">\lim_{n\rightarrow \infty} \frac{a_n}{b_n}=L,</math>&nbsp; where &nbsp;<math style="vertical-align: -1px">L</math> &nbsp;is a positive real number,
 |-
-|&nbsp; &nbsp; &nbsp; &nbsp; then &nbsp;<math>\sum_{n=1}^\infty a_n</math>&nbsp; and &nbsp;<math>\sum_{n=1}^\infty b_n</math>&nbsp; either both converge or both diverge.
+|&nbsp; &nbsp; &nbsp; &nbsp; then &nbsp;<math style="vertical-align: -20px">\sum_{n=1}^\infty a_n</math>&nbsp; and &nbsp;<math style="vertical-align: -20px">\sum_{n=1}^\infty b_n</math>&nbsp; either both converge or both diverge.
 |}
@@ Line 29: / Line 29: @@
 |This means that we can use a comparison test on this series.
 |-
-|Let &nbsp;<math style="vertical-align: -14px">a_n=\frac{n^3+7n}{\sqrt{1+n^{10}}}.</math>
+|Let &nbsp;<math style="vertical-align: -19px">a_n=\frac{n^3+7n}{\sqrt{1+n^{10}}}.</math>
 |}

@@ Line 1: / Line 1: @@
 <span class="exam">Test if the following series converges or diverges. Give reasons and clearly state if you are using any standard test.
-::::<math>\sum_{n=1}^{\infty} \frac{n^3+7n}{\sqrt{1+n^{10}}}</math>
+::<math>\sum_{n=1}^{\infty} \frac{n^3+7n}{\sqrt{1+n^{10}}}</math>
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
@@ Line 16: / Line 16: @@
+|
 |}
 '''Solution:'''
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
@@ Line 39: / Line 38: @@
 |}
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 !Final Answer: &nbsp;
 |-
-|&nbsp;&nbsp; '''(a)'''
+|&nbsp;&nbsp;
 |}
 [[009C_Sample_Final_3|'''<u>Return to Sample Exam</u>''']]

@@ Line 1: / Line 1: @@
-<span class="exam">Compute
+<span class="exam">Test if the following series converges or diverges. Give reasons and clearly state if you are using any standard test.
-::<span class="exam">a) <math style="vertical-align: -12px">\lim_{n\rightarrow \infty} \frac{3-2n^2}{5n^2+n+1}</math>
+::::<math>\sum_{n=1}^{\infty} \frac{n^3+7n}{\sqrt{1+n^{10}}}</math>
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"