# How do you find the power series representation for the function #f(x)=1/(1-x)# ?

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To find the power series representation for the function ( f(x) = \frac{1}{1-x} ), you can use the geometric series formula. The geometric series formula states that for ( |x| < 1 ),

[ \frac{1}{1 - x} = \sum_{n=0}^{\infty} x^n ]

This is a well-known result derived from the geometric series formula. So, the power series representation for ( f(x) = \frac{1}{1-x} ) is

[ f(x) = \sum_{n=0}^{\infty} x^n ]

for ( |x| < 1 ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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