# Calculus Examples

Find the Sum of the First 4 Terms
, ,
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
Apply the product rule to .
Step 5
One to any power is one.
Step 6
Combine and .
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
Simplify the numerator.
Step 9.1
Apply the product rule to .
Step 9.2
One to any power is one.
Step 9.3
Raise to the power of .
Step 9.4
To write as a fraction with a common denominator, multiply by .
Step 9.5
Combine and .
Step 9.6
Combine the numerators over the common denominator.
Step 9.7
Simplify the numerator.
Step 9.7.1
Multiply by .
Step 9.7.2
Subtract from .
Step 9.8
Move the negative in front of the fraction.
Step 10
Simplify the denominator.
Step 10.1
To write as a fraction with a common denominator, multiply by .
Step 10.2
Combine and .
Step 10.3
Combine the numerators over the common denominator.
Step 10.4
Simplify the numerator.
Step 10.4.1
Multiply by .
Step 10.4.2
Subtract from .
Step 10.5
Move the negative in front of the fraction.
Step 11
Dividing two negative values results in a positive value.
Step 12
Multiply the numerator by the reciprocal of the denominator.
Step 13
Cancel the common factor of .
Step 13.1
Factor out of .
Step 13.2
Cancel the common factor.
Step 13.3
Rewrite the expression.
Step 14
Cancel the common factor of .
Step 14.1
Factor out of .
Step 14.2
Cancel the common factor.
Step 14.3
Rewrite the expression.
Step 15
Cancel the common factor of .
Step 15.1
Factor out of .
Step 15.2
Factor out of .
Step 15.3
Cancel the common factor.
Step 15.4
Rewrite the expression.
Step 16
Combine and .
Step 17
Multiply by .
Step 18
Convert the fraction to a decimal.