Infinite Series

An infinite series has an infinite number of terms.

The sum of the first n terms, Sn , is called a partial sum.

If Sn tends to a limit as n tends to infinity, the limit is called the sum to infinity of the

series.

Arithmetic series

As n tends to infinity, Sn tends to

The sum to infinity for an arithmetic series is undefined.

Geometric series

When r > 1, rn tends to infinity as n tends to infinity.

When r < 1, rn tends to zero as n tends to infinity.

The sum to infinity for a geometric series is undefined

when

The sum to infinity for a geometric series

when

is