**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.

Noah Dana-Picard
2007-12-28