Finite Math Examples

Solve for x a(n)=1/3*(1-(-1/2)^(n-1))
Step 1
Simplify.
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Step 1.1
Simplify each term.
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Step 1.1.1
Use the power rule to distribute the exponent.
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Step 1.1.1.1
Apply the product rule to .
Step 1.1.1.2
Apply the product rule to .
Step 1.1.2
Multiply by by adding the exponents.
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Step 1.1.2.1
Move .
Step 1.1.2.2
Multiply by .
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Step 1.1.2.2.1
Raise to the power of .
Step 1.1.2.2.2
Use the power rule to combine exponents.
Step 1.1.2.3
Combine the opposite terms in .
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Step 1.1.2.3.1
Add and .
Step 1.1.2.3.2
Add and .
Step 1.1.3
One to any power is one.
Step 1.1.4
Combine and .
Step 1.2
Apply the distributive property.
Step 1.3
Multiply by .
Step 1.4
Combine.
Step 1.5
Multiply by .
Step 2
Divide each term in by and simplify.
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Step 2.1
Divide each term in by .
Step 2.2
Simplify the left side.
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Step 2.2.1
Cancel the common factor of .
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Step 2.2.1.1
Cancel the common factor.
Step 2.2.1.2
Divide by .
Step 2.3
Simplify the right side.
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Step 2.3.1
Combine the numerators over the common denominator.
Step 2.3.2
Simplify the numerator.
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Step 2.3.2.1
To write as a fraction with a common denominator, multiply by .
Step 2.3.2.2
Multiply by .
Step 2.3.2.3
Combine the numerators over the common denominator.
Step 2.3.3
Multiply the numerator by the reciprocal of the denominator.
Step 2.3.4
Multiply by .
Step 2.3.5
Reorder factors in .