MathAdmin at 14:54, 20 April 2017

2017-04-20T14:54:59Z

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2017-04-09T19:28:53Z

Created page with "'''This is a sample, and is meant to represent the material usually covered in Math 9C for the midterm. An actual test may or may not be similar.''' '''Click on the''' '''<s..."

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'''This is a sample, and is meant to represent the material usually covered in Math 9C for the midterm. An actual test may or may not be similar.'''

'''Click on the''' ''' boxed problem numbers  to go to a solution.'''
<div class="noautonum">TOC</div>

== [[009C_Sample Midterm 2,_Problem_1| Problem 1 ]] ==
 Evaluate:

(a)  <math>\lim _{n\rightarrow \infty} \frac{1}{\big(\frac{n-4}{n}\big)^n}</math>

(b)  <math>\sum_{n=1}^\infty \frac{1}{2} \bigg(\frac{1}{4}\bigg)^{n-1} </math>

== [[009C_Sample Midterm 2,_Problem_2| Problem 2 ]] ==
Determine convergence or divergence:

::<math>\sum_{n=1}^\infty \frac{3^n}{n}</math>

== [[009C_Sample Midterm 2,_Problem_3| Problem 3 ]] ==
 Determine convergence or divergence:

(a)  <math>\sum_{n=1}^\infty (-1)^n \sqrt{\frac{1}{n}}</math>

(b)  <math>\sum_{n=1}^\infty (-2)^n \frac{n!}{n^n} </math>

== [[009C_Sample Midterm 2,_Problem_4| Problem 4 ]] ==
 Find the radius of convergence and interval of convergence of the series.

(a)  <math>\sum_{n=1}^\infty n^nx^n</math>

(b)  <math>\sum_{n=1}^\infty \frac{(x+1)^n}{\sqrt{n}}</math>

== [[009C_Sample Midterm 2,_Problem_5| Problem 5 ]] ==
 If  <math>\sum_{n=0}^\infty c_nx^n</math>  converges, does it follow that the following series converges?

(a)  <math>\sum_{n=0}^\infty c_n\bigg(\frac{x}{2}\bigg)^n</math>

(b)  <math>\sum_{n=0}^\infty c_n(-x)^n </math>

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	<span class="exam">(b)  <math>\sum_{n=0}^\infty c_n(-x)^n </math>		<span class="exam">(b)  <math>\sum_{n=0}^\infty c_n(-x)^n </math>
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		+	'''Contributions to this page were made by [[Contributors\|Kayla Murray]]'''