# Find the Sum of the Series 1/2 , -1/4 , 1/8 , -1/16 , , ,
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 .
Use the power rule to distribute the exponent.
Apply the product rule to .
Apply the product rule to .
One to any power is one.
Combine and .
Multiply .
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 .
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 .
Simplify the numerator.
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.
Simplify the denominator.
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.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply .
Multiply and .
Multiply by .
Find the Sum of the Series 1/2 , -1/4 , 1/8 , -1/16     