Geom Series: Converge Radius 1, c Complex Num

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SUMMARY

The discussion focuses on expressing the function f(z) = 1/(c(1+z)) as a geometric series with a radius of convergence of 1, where c is a complex number. The key formula referenced is 1/(1-z) = 1 + z + z² + z³ + ..., which serves as the foundational basis for constructing the series. Mastery of this concept is emphasized as essential for understanding infinite series in complex analysis.

PREREQUISITES
  • Understanding of complex numbers and their properties
  • Familiarity with geometric series and their convergence
  • Knowledge of the formula for geometric series: 1/(1-z)
  • Basic principles of infinite series in calculus
NEXT STEPS
  • Study the derivation of the geometric series formula in detail
  • Explore the implications of radius of convergence in complex analysis
  • Learn about the convergence criteria for infinite series
  • Investigate applications of geometric series in solving complex functions
USEFUL FOR

Students and professionals in mathematics, particularly those focusing on complex analysis, as well as educators teaching infinite series and geometric series concepts.

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how can I write f(z)= 1/(c(1+z)) as a geometric series with radius of convergence 1, where c is a complex number?
 
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this is the one series most people know.

hint: 1/(1-z) = 1 + z + z^2 + z^3+...


if you learn this, you are a master of infinites eries. i.e. there is nothing else to know.
 
thanks i see it now
 

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