Math Help - Power Series

A power series is a series of the form:

where a and  c _i (i = positive integers such as 1, 2, 3, etc) are constant.

Power series can be written as:

 or or

Convergence of power series

A power series is said to converge:

• at x 1 if and only if converges.
• on the set S if and only if converges for each x in S.

If converges at then it converges absolutely whenever | x | < |x ₁ |.

Divergence of power series

If diverges at x ₁, then it divergest for all |x| > |x ₁ |.