4.3. Special Series
Theorem 4.2.9: Geometric Series
Let a be any real number. Then the series is called Geometric Series.
- if | a | < 1 the geometric series converges
- if | a | 1 the geometric series diverges
The proof consists of a nice trick. Consider the partial sum S N and multiply it by a:
- S N = 1 + a + a 2 + a 3 + ... + a N
- a S N = a + a 2 + a 3 + ... + a N+1