Calculus Examples

Find the Sum of the First 4 Terms
, ,
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 .
One to any power is one.
Multiply by to get .
Simplify .
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Write as a fraction with denominator .
Multiply and to get .
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.
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Apply the product rule to .
One to any power is one.
Raise to the power of to get .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine the numerators over the common denominator.
Multiply by to get .
Subtract from to get .
Move the negative in front of the fraction.
Simplify the denominator.
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Remove parentheses.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine the numerators over the common denominator.
Multiply by to get .
Subtract from to get .
Move the negative in front of the fraction.
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
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Rewrite.
Rewrite.
Factor out the greatest common factor .
Cancel the common factor.
Rewrite the expression.
Simplify.
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Multiply by to get .
Multiply and to get .
Multiply by to get .
Multiply by to get .
Reduce the expression by cancelling the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Write as a fraction with denominator .
Factor out the greatest common factor .
Cancel the common factor.
Rewrite the expression.
Simplify.
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Multiply and to get .
Multiply by to get .
Convert the fraction to a decimal.
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