# Trigonometry Examples

Find the Sum of the Series 1-1/3+1/9-1/27+1/81
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 .
Multiply by .
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 .
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 .
Multiply by .
Multiply the numerator and denominator of the complex fraction by .
Multiply by .
Combine.
Apply the distributive property.
Cancel the common factor of .
Move the leading negative in into the numerator.
Cancel the common factor.
Rewrite the expression.
Simplify the numerator.
Use the power rule to distribute the exponent.
Apply the product rule to .
Apply the product rule to .
Anything raised to is .
Multiply by .
Anything raised to is .
Anything raised to is .
Divide by .
Multiply by .
Multiply by .
Subtract from .
Simplify the denominator.
Multiply by .
Subtract from .
Divide by .