Calculus Examples

Find the Sum of the Infinite Geometric Series
, ,
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 to get .
Simplify the equation to find .
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Simplify the denominator.
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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 the numerators over the common denominator.
Multiply by to get .
Multiply by to get .
Subtract from to get .
Multiply the numerator by the reciprocal of the denominator.
Simplify .
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Write as a fraction with denominator .
Multiply and to get .
Multiply by to get .
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