Difference between revisions of "Mock AIME 2 2006-2007 Problems/Problem 5"

 
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Given that <math>\displaystyle  iz^2=1+\frac 2z + \frac{3}{z^2}+\frac{4}{z ^3}+\frac{5}{z^4}+\cdots</math> and <math>\displaystyle z=a\pm \sqrt{b+i},</math> find <math>\displaystyle  \lfloor 100ab \rfloor.</math>
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==Problem==
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Given that <math>\displaystyle  iz^2=1+\frac 2z + \frac{3}{z^2}+\frac{4}{z ^3}+\frac{5}{z^4}+\cdots</math> and <math>\displaystyle z=n\pm \sqrt{-i},</math> find <math>\displaystyle  \lfloor 100n \rfloor.</math>

Revision as of 13:05, 25 July 2006

Problem

Given that $\displaystyle  iz^2=1+\frac 2z + \frac{3}{z^2}+\frac{4}{z ^3}+\frac{5}{z^4}+\cdots$ and $\displaystyle z=n\pm \sqrt{-i},$ find $\displaystyle  \lfloor 100n \rfloor.$

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