Difference between revisions of "009C Sample Midterm 1, Problem 3"

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<span class="exam">Determine whether the following series converges absolutely, conditionally or whether it diverges.
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<span class="exam"> Determine whether the following series converges absolutely,  
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<span class="exam"> conditionally or whether it diverges.
  
 
<span class="exam"> Be sure to justify your answers!
 
<span class="exam"> Be sure to justify your answers!
  
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::::::<math>\sum_{n=1}^\infty \frac{(-1)^n}{n}</math>
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::<math>\sum_{n=1}^\infty \frac{(-1)^n}{n}</math>
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!Foundations: &nbsp;
 
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|'''1.''' A series <math>\sum a_n</math> is '''absolutely convergent''' if
 
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|&nbsp; &nbsp; &nbsp; &nbsp; the series <math>\sum |a_n|</math> converges.
 
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|'''2.''' A series <math>\sum a_n</math> is '''conditionally convergent''' if
 
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|&nbsp; &nbsp; &nbsp; &nbsp; the series <math>\sum |a_n|</math> diverges and
 
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|&nbsp; &nbsp; &nbsp; &nbsp; the series <math>\sum a_n</math> converges.
 
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'''Solution:'''
 
  
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!Step 1: &nbsp;
 
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<hr>
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!Step 2: &nbsp;
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[[009C Sample Midterm 1, Problem 3 Solution|'''<u>Solution</u>''']]
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[[009C Sample Midterm 1, Problem 3 Detailed Solution|'''<u>Detailed Solution</u>''']]
  
  
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!Final Answer: &nbsp;
 
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[[009C_Sample_Midterm_1|'''<u>Return to Sample Exam</u>''']]
 
[[009C_Sample_Midterm_1|'''<u>Return to Sample Exam</u>''']]

Latest revision as of 22:54, 11 November 2017

Determine whether the following series converges absolutely,

conditionally or whether it diverges.

Be sure to justify your answers!

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sum_{n=1}^\infty \frac{(-1)^n}{n}}


Solution


Detailed Solution


Return to Sample Exam

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