Evaluate the geometric series or state that it diverges. one ninth 1 9plus+startfraction 7 over 81 endfraction 7 81plus+startfraction 49 over 729 endfraction 49 729plus+startfraction 343 over 6561 endfraction 343 6561plus+

In the given geometric series, r, the common ratio is 7/9; therefore the series is convergent.  

Step-by-step explanation:

We are given the geometric series:

The general geometric series is in the for , where a is the first term and r is the common ratio.

Comparing with the given geometric series, we have,

If r > 1, the series is divergent.  

If r < 1, the series is convergent.

In the given geometric series, r, the common ratio is 7/9; therefore the series is convergent.