Calculus Examples

Find the Sum of the Infinite Geometric Series
, ,
Step 1
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:
Step 2
The sum of a series is calculated using the formula . For the sum of an infinite geometric series , as approaches , approaches . Thus, approaches .
Step 3
The values and can be put in the equation .
Step 4
Simplify the equation to find .
Simplify the denominator.
Write as a fraction with a common denominator.
Combine the numerators over the common denominator.
Subtract from .
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .