Calculus II: Prperties of congergent series

1. Properties of convergent series

We can add, subtract convergent series. We can multiply a convergent series by a real number. The result is a convergent series.

If {a_n} and {b_n} are two convergent series, and c is real number:

{a_n + b_n} = {a_n} + {b_n}
is a convergent series

{a_n - b_n} = {a_n} - {b_n}
is a convergent series

{c(a_n)} = c {a_n}
is a convergent series

If one of them diverges
their combination diverges.

If both of the series diverge
their combination converges or diverges.

2. Examples

3. Exercises