nannagarvey2501 nannagarvey2501
  • 01-08-2017
  • Mathematics
contestada

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

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LammettHash
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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