# Calculus Examples

, ,

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 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 .