2.4 Continuity

1
Power Series
CHAPTER 2
2.4 Continuity
A power series is a series of the form ?
?n0 cn xn c0 c1 x c2 x 2 c3 x 3
where x is a variable and the cns are
constants called the coefficients of the series.
2
CHAPTER 2

• Theorem For a given power series
  ? ?n0 cn (x - a)n there are only three
  possibilities
• The series converges only when x a.
• The series converges for all x.
• There is a positive number R such that the
  series converges if x a lt R and diverges if
  x a gt R.

2.4 Continuity