# 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.

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 .

Multiply by .

Subtract from .

Multiply the numerator by the reciprocal of the denominator.

Simplify .

Write as a fraction with denominator .

Multiply and .

Multiply by .