Find the sum of the series. 1 + z/5 + z^2/25 + z^3.125

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01-08-2017
Mathematics

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Find the sum of the series. 1 + z/5 + z^2/25 + z^3.125

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LammettHash LammettHash · Answer 1 · 2017-08-01T19:05:39+02:00

LammettHash LammettHash

01-08-2017

[tex]1+\dfrac z5+\dfrac{z^2}{25}+\dfrac{z^3}{125}+\cdots=\displaystyle\sum_{k=0}^\infty\left(\frac z5\right)^k[/tex]
[tex]=\dfrac1{1-\frac z5}=\dfrac5{5-z}[/tex]

provided that [tex]\left|\dfrac z5\right|<1\iff|z|<5[/tex].

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