Infinite Geometric Series

In this section of Algebra Homework Help, we discuss infinite geometric series and the general form of infinite geometric series. From the previous section, we know the general form of the sum of geometric series.

Sum to infinity of geometric series

When n is so large and r is greater than one, then the following two terms in infinite geometric series will be very large:

,

Therefore:

will tend towards infinity as n tends towards infinity.

Infinite geometric series converges

However, if r is less than one then the sum to infinity of a geometric series is finite. As n increases rⁿ decreases for r<1 and tends towards zero as n tends towards infinity.