$\"\"$

The sum of an infinete geometric series is $\"\"$ , with $\"\"$ ,

Where $\"\"$ is first term and r is common ratio.

The infinite geometric series is $\"\"$

In the above series $\"\"$ .

$\"\"$ , the sum exists. $\"\"$

$\"\"$ (Substitute $\"\"$ )

$\"\"$ (Product of two same signs is positive)

$\"\"$ (Add denominator: $\"\"$ )

= 1 (Divide: $\"\"$ ) $\"\"$

The sum of the infinite geometric series is 1.