Difference between revisions of "009C Sample Midterm 2, Problem 5"

Latest revision as of 11:42, 12 November 2017

If $\sum _{n=0}^{\infty }c_{n}x^{n}$ converges, does it follow that the following series converges?

(a) $\sum _{n=0}^{\infty }c_{n}{\bigg (}{\frac {x}{2}}{\bigg )}^{n}$

(b) $\sum _{n=0}^{\infty }c_{n}(-x)^{n}$

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+[[009C Sample Midterm 2, Problem 5 Solution|'''<u>Solution</u>''']]
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Foundations: &nbsp;
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-|If a power series converges, then it has a nonempty interval of convergence.
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+[[009C Sample Midterm 2, Problem 5 Detailed Solution|'''<u>Detailed Solution</u>''']]
-'''Solution:'''
-'''(a)'''
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-!Step 1: &nbsp;
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-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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-'''(b)'''
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-!Step 1: &nbsp;
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-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Final Answer: &nbsp;
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-|&nbsp; &nbsp; '''(a)''' &nbsp; &nbsp;
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-|&nbsp; &nbsp; '''(b)''' &nbsp; &nbsp;
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 [[009C_Sample_Midterm_2|'''<u>Return to Sample Exam</u>''']]