Difference between revisions of "009C Sample Final 2, Problem 7"

Latest revision as of 18:33, 2 December 2017

(a) Consider the function $f(x)={\bigg (}1-{\frac {1}{2}}x{\bigg )}^{-2}.$ Find the first three terms of its Binomial Series.

(b) Find its radius of convergence.

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 <span class="exam">(b) Find its radius of convergence.
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-'''(a)'''
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-|The Maclaurin series of &nbsp;<math>\frac{1}{(1-x)^2}</math>&nbsp; is
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-|&nbsp; &nbsp; &nbsp; &nbsp;<math>\sum_{n=0}^\infty (n+1)x^n.</math>
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-|So, the Maclaurin series of &nbsp;<math>\frac{1}{(1-\frac{1}{2}x)^2}</math>&nbsp; is
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-|&nbsp; &nbsp; &nbsp; &nbsp;<math>\sum_{n=0}^\infty (n+1)\bigg(\frac{1}{2}x\bigg)^n=\sum_{n=0}^\infty \frac{(n+1)x^n}{2^n}.</math>
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-|&nbsp;&nbsp; '''(a)'''
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-|&nbsp;&nbsp; '''(b)'''
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 [[009C_Sample_Final_2|'''<u>Return to Sample Exam</u>''']]