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Question Number 183536 by SANOGO last updated on 26/Dec/22

$$radiusofconvergenceofserie:$$$$\sum _{nϵN}\frac{cos\left(\frac{3\pi }{3}\right)}{5^n}{z}^n$$

Commented by mr W last updated on 26/Dec/22

$$strange!$$$$whydoyouwrite\frac{3\pi }{3}?notdirectly\pi ?$$$$\cos \left(\frac{3\pi }{3}\right)=\cos \pi =-1$$

Answered by aleks041103 last updated on 27/Dec/22

$$=-\underset{n=1}{\sum ^{\mathrm{\infty }}}{\left(\frac{z}{5}\right)}^n$$$$thisisageometricseries.$$$$toconverge,\mid \frac{z}{5}\mid <1$$$$\Rightarrow \mid z\mid <5$$

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