# 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:

This is the form of a geometric sequence.

Substitute in the values of and .

Apply the product rule to .

One to any power is one.

Multiply by .

Write as a fraction with denominator .

Multiply and .

This is the formula to find the sum of the first terms of the geometric sequence. To evaluate it, find the values of and .

Replace the variables with the known values to find .

Apply the product rule to .

One to any power is one.

Raise to the power of .

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.

Simplify the numerator.

Move the negative in front of the fraction.

Remove parentheses.

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.

Simplify the numerator.

Move the negative in front of the fraction.

Multiply the numerator by the reciprocal of the denominator.

Rewrite.

Rewrite.

Factor out the greatest common factor .

Cancel the common factor.

Rewrite the expression.

Multiply by .

Multiply and .

Multiply by .

Multiply by .

Reduce the expression by cancelling the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Write as a fraction with denominator .

Factor out the greatest common factor .

Cancel the common factor.

Rewrite the expression.

Multiply and .

Multiply by .

Divide by .

Convert the fraction to a decimal.