# 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 to get .

Write as a fraction with denominator .

Multiply and to get .

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 get .

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.

Multiply by to get .

Subtract from to get .

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.

Multiply by to get .

Subtract from to get .

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 to get .

Multiply and to get .

Multiply by to get .

Multiply by to get .

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 to get .

Multiply by to get .

Convert the fraction to a decimal.