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