$\"\"$

Explain why an infinite geometric series will not have a sum if $\"\"$ .

The sum for infinite geometric series is $\"\"$ .

If $\"\"$ then the sum of the series increases without limit.

Therefore, the corresponding sequence will be divergent, and the sum of the series cannot be calculated.

Consider the geometric series is $\"\"$ .

The common ration is $\"\"$ .

The sum of the series is $\"\"$ .

$\"\"$ .

$\"\"$

Consider the geometric series $\"\"$ .

The common ratio is $\"\"$ .

The sum of the series is $\"\"$ .

$\"\"$ .

Therefore, the value $\"\"$ is not the correct value for sum. \ \

Therefore, the formula for the sum of an infinite geometric series does not work when $\"\"$ .

$\"\"$

The formula for the sum of an infinite geometric series does not work when $\"\"$ . \ \