, , ,

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 .

Apply the product rule to .

One to any power is one.

Combine and .

Multiply and .

Multiply by by adding the exponents.

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Combine the opposite terms in .

Subtract from .

Add 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 .

Use the power rule to distribute the exponent.

Apply the product rule to .

Apply the product rule to .

Raise to the power of .

Multiply by .

One to any power is one.

Raise to the power of .

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Subtract from .

Move the negative in front of the fraction.

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Subtract from .

Move the negative in front of the fraction.

Dividing two negative values results in a positive value.

Multiply the numerator by the reciprocal of the denominator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply and .

Multiply by .

Find the Sum of the Series 1/2 , -1/4 , 1/8 , -1/16