Geometric Series

analysis

Definition

Geometric Series

A series of form:

is called geometric series.

Convergence

For , the value of the geometric series is given by:

Proof

Let , thus . Given that the sequence is convergent and its limit is , the series is convergent.

Let be the series’ partial sum.

Thus:

Divergence

For , the geometric series is divergent, since the sequence of terms, i.e., is not a null sequence.