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Calculus Examples
, , , ,
Step 1
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:
Step 2
This is the form of a geometric sequence.
Step 3
Substitute in the values of and .
Step 4
Multiply by .
Step 5
Apply the product rule to .
Step 6
One to any power is one.
Step 7
This is the formula to find the sum of the first terms of the geometric sequence. To evaluate it, find the values of and .
Step 8
Replace the variables with the known values to find .
Step 9
Multiply by .
Step 10
Step 10.1
Multiply by .
Step 10.2
Combine.
Step 11
Apply the distributive property.
Step 12
Step 12.1
Cancel the common factor.
Step 12.2
Rewrite the expression.
Step 13
Step 13.1
Apply the product rule to .
Step 13.2
Cancel the common factor of .
Step 13.2.1
Factor out of .
Step 13.2.2
Cancel the common factor.
Step 13.2.3
Rewrite the expression.
Step 13.3
One to any power is one.
Step 13.4
Raise to the power of .
Step 13.5
Multiply by .
Step 13.6
To write as a fraction with a common denominator, multiply by .
Step 13.7
Combine and .
Step 13.8
Combine the numerators over the common denominator.
Step 13.9
Simplify the numerator.
Step 13.9.1
Multiply by .
Step 13.9.2
Subtract from .
Step 13.10
Move the negative in front of the fraction.
Step 14
Step 14.1
Multiply by .
Step 14.2
Subtract from .
Step 15
Step 15.1
Dividing two negative values results in a positive value.
Step 15.2
Divide by .