MathAdmin at 14:55, 20 April 2017

2017-04-20T14:55:43Z

MathAdmin: 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''' '''
2017-04-09T19:25:36Z

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 1,_Problem_1| Problem 1 ]] ==
 Does the following sequence converge or diverge?

 If the sequence converges, also find the limit of the sequence.

 Be sure to jusify your answers!

::<math>a_n=\frac{\ln n}{n}</math>

== [[009C_Sample Midterm 1,_Problem_2| Problem 2 ]] ==
 Consider the infinite series  <math>\sum_{n=2}^\infty 2\bigg(\frac{1}{2^n}-\frac{1}{2^{n+1}}\bigg).</math>

(a) Find an expression for the  <math style="vertical-align: 0px">n</math>th partial sum  <math style="vertical-align: -3px">s_n</math>  of the series.

(b) Compute  <math style="vertical-align: -11px">\lim_{n\rightarrow \infty} s_n.</math>

== [[009C_Sample Midterm 1,_Problem_3| Problem 3 ]] ==
 Determine whether the following series converges absolutely,

 conditionally or whether it diverges.

 Be sure to justify your answers!

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

== [[009C_Sample Midterm 1,_Problem_4| Problem 4 ]] ==
 Determine the convergence or divergence of the following series.

 Be sure to justify your answers!

::<math>\sum_{n=1}^\infty \frac{1}{n^23^n}</math>

== [[009C_Sample Midterm 1,_Problem_5| Problem 5 ]] ==
 Find the radius of convergence and interval of convergence of the series.

(a)  <math>\sum_{n=0}^\infty \sqrt{n}x^n</math>

(b)  <math>\sum_{n=0}^\infty (-1)^n \frac{(x-3)^n}{2n+1}</math>

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	<span class="exam">(b)  <math>\sum_{n=0}^\infty (-1)^n \frac{(x-3)^n}{2n+1}</math>		<span class="exam">(b)  <math>\sum_{n=0}^\infty (-1)^n \frac{(x-3)^n}{2n+1}</math>
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		+	'''Contributions to this page were made by [[Contributors\|Kayla Murray]]'''