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Sahithyan's S1

Power Series

A series of the form:

Here:

  • - a variable
  • - a constant

Convergence of a power series can be checked using root test.

Radius of convergence

Maximum radius of in where the series converges.

The below equation can be used to find :

Range of convergence

is the range of convergence.

Theorem 1

If and for , then is uniformly (and absolutely) converging.