# How to graph #\sum_{n=0}^\oo 2x^n#?

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To graph the function ( \sum_{n=0}^\infty 2x^n ), follow these steps:

- Recognize that this function represents a geometric series.
- The formula for the sum of an infinite geometric series is ( S = \frac{a}{1 - r} ), where ( a ) is the first term and ( r ) is the common ratio.
- In this case, ( a = 2 ) and ( r = x ).
- However, for ( |x| < 1 ), the series converges. Therefore, consider the domain as ( |x| < 1 ).
- Substitute the values into the formula to get ( S = \frac{2}{1 - x} ).
- Now, plot the graph of ( S = \frac{2}{1 - x} ) for ( |x| < 1 ).

That's how you graph ( \sum_{n=0}^\infty 2x^n ).

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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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