# Find the Sum of the Infinite Geometric Series 2 , 1/2 , 1/8 , 1/32

, , ,
This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by gives the next term. In other words, .
Geometric Sequence:
The sum of a series is calculated using the formula . For the sum of an infinite geometric series , as approaches , approaches . Thus, approaches .
The values and can be put in the equation .
Simplify the equation to find .
Simplify the denominator.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Multiply the numerator by the reciprocal of the denominator.
Multiply .
Combine and .
Multiply by .
Find the Sum of the Infinite Geometric Series 2 , 1/2 , 1/8 , 1/32

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