$\"\"$

The given geometric series $\"\"$ .

The sum of a geometric series is $\"\"$ ,

The first term of the sequence $\"\"$ and r is common ratio.

$\"\"$

Method 1

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

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

$\"\"$ (Add denominator: 1 + 2 = 3)

$\"\"$ (Evaluate powers: $\"\"$ )

$\"\"$ (Subtract numerator: $\"\"$ )

Divide: $\"\"$ .

$\"\"$

The sum of the geometric series is 455.