# Calculus Examples

, ,

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

Step 4.1

Simplify the denominator.

Step 4.1.1

Write as a fraction with a common denominator.

Step 4.1.2

Combine the numerators over the common denominator.

Step 4.1.3

Subtract from .

Step 4.2

Multiply the numerator by the reciprocal of the denominator.

Step 4.3

Cancel the common factor of .

Step 4.3.1

Factor out of .

Step 4.3.2

Cancel the common factor.

Step 4.3.3

Rewrite the expression.

Step 4.4

Multiply by .