Difference between revisions of "009C Sample Final 3, Problem 6"

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(Created page with "<span class="exam">Compute ::<span class="exam">a) <math style="vertical-align: -12px">\lim_{n\rightarrow \infty} \frac{3-2n^2}{5n^2+n+1}</math> ::<span class="exam">b) <mat...")
 
 
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<span class="exam">Compute
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<span class="exam"> Consider the power series
  
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::<span class="exam">a) <math style="vertical-align: -12px">\lim_{n\rightarrow \infty} \frac{3-2n^2}{5n^2+n+1}</math>
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::<math>\sum_{n=0}^\infty (-1)^n \frac{x^{n+1}}{n+1}.</math>
  
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::<span class="exam">b) <math style="vertical-align: -12px">\lim_{n\rightarrow \infty} \frac{\ln n}{\ln 3n}</math>
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<span class="exam">(a) Find the radius of convergence of the above power series.
  
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<span class="exam">(b) Find the interval of convergence of the above power series.
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!Foundations: &nbsp;
 
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'''Solution:'''
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<span class="exam">(c) Find the closed formula for the function &nbsp;<math style="vertical-align: -5px">f(x)</math>&nbsp; to which the power series converges.
  
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'''(a)'''
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<span class="exam">(d) Does the series
  
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::<math>\sum_{n=0}^\infty \frac{1}{(n+1)3^{n+1}}</math>
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!Step 1: &nbsp;
 
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<span class="exam">converge?
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!Step 2: &nbsp;
 
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'''(b)'''
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[[009C Sample Final 3, Problem 6 Solution|'''<u>Solution</u>''']]
  
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!Step 1: &nbsp;
 
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[[009C Sample Final 3, Problem 6 Detailed Solution|'''<u>Detailed Solution</u>''']]
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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 16:21, 3 December 2017

Consider the power series

(a) Find the radius of convergence of the above power series.

(b) Find the interval of convergence of the above power series.

(c) Find the closed formula for the function    to which the power series converges.

(d) Does the series

converge?

Solution


Detailed Solution


Return to Sample Exam

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