# How do you write a geometric series for which r=1/2 and n=4?

Hence: the series requested is:

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To write a geometric series where the common ratio (r) is 1/2 and the number of terms (n) is 4, you can use the formula:

[S = a \left( \frac{1 - r^n}{1 - r} \right)]

Where:

- (S) represents the sum of the series,
- (a) is the first term of the series,
- (r) is the common ratio,
- (n) is the number of terms.

Substitute the given values into the formula:

[a = \text{first term}] [r = \frac{1}{2}] [n = 4]

[S = a \left( \frac{1 - \left( \frac{1}{2} \right)^4}{1 - \frac{1}{2}} \right)]

[S = a \left( \frac{1 - \frac{1}{16}}{1 - \frac{1}{2}} \right)]

[S = a \left( \frac{\frac{15}{16}}{\frac{1}{2}} \right)]

[S = a \left( \frac{15}{8} \right)]

This gives you the general form of the sum of the geometric series with (r = \frac{1}{2}) and (n = 4), expressed in terms of the first term (a).

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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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