Difference between revisions of "009C Sample Final 3, Problem 2"

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<span class="exam">(b) Test if the series converges conditionally. Give reasons for your answer.
 
<span class="exam">(b) Test if the series converges conditionally. Give reasons for your answer.
  
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!Foundations: &nbsp;
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[[009C Sample Final 3, Problem 2 Solution|'''<u>Solution</u>''']]
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|'''1.''' A series &nbsp;<math>\sum a_n</math>&nbsp; is '''absolutely convergent''' if
 
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|&nbsp; &nbsp; &nbsp; &nbsp; the series &nbsp;<math>\sum |a_n|</math>&nbsp; converges.
 
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|'''2.''' A series &nbsp;<math>\sum a_n</math>&nbsp; is '''conditionally convergent''' if
 
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|&nbsp; &nbsp; &nbsp; &nbsp; the series &nbsp;<math>\sum |a_n|</math>&nbsp; diverges and the series &nbsp;<math>\sum a_n</math>&nbsp; converges.
 
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'''Solution:'''
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[[009C Sample Final 3, Problem 2 Detailed Solution|'''<u>Detailed Solution</u>''']]
  
'''(a)'''
 
  
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!Step 1: &nbsp;
 
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!Step 2: &nbsp;
 
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'''(b)'''
 
 
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!Step 1: &nbsp;
 
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!Step 2: &nbsp;
 
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!Final Answer: &nbsp;
 
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|&nbsp;&nbsp; '''(a)'''
 
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|&nbsp;&nbsp; '''(b)'''
 
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[[009C_Sample_Final_3|'''<u>Return to Sample Exam</u>''']]
 
[[009C_Sample_Final_3|'''<u>Return to Sample Exam</u>''']]

Latest revision as of 18:41, 2 December 2017

Consider the series

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=2}^\infty \frac{(-1)^n}{\sqrt{n}}.}

(a) Test if the series converges absolutely. Give reasons for your answer.

(b) Test if the series converges conditionally. Give reasons for your answer.


Solution


Detailed Solution


Return to Sample Exam