Step 1:

The series is $\"\"$

The above series is geometric series with common ratio 0.9.

The geometric series $\"\"$ is convergent if $\"\"$ and if $\"\"$ , the geometric series is

divergent.

Here $\"\"$ and common ratio $\"\"$ .

Hence the geometric series $\"\"$ is convergent.

Solution:

The infinite series $\"\"$ is convergent.