# The algebra of convergent series.

Theorem 9.2.1   Let and be two convergent series. Then the series is convergent and its sum is equal to .

Theorem 9.2.2   Let be a convergent series and . Then the series is convergent and its sum is equal to .

Together these two theorems mean that the set of convergent series of real numbers is a real vector space.

Remark 9.2.3   Adding or deleting terms from a series does not change the convergence/divergence. For a convergent series, it changes the value of the sum.

Example 9.2.4

Noah Dana-Picard 2007-12-28