# How do you find #S_n# for the geometric series #a_2=-36#, a_5=972#, n=7?

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To find (S_n) for a geometric series, you can use the formula:

[ S_n = a_1 \frac{{1 - r^n}}{{1 - r}} ]

Where:

- (S_n) is the sum of the first (n) terms,
- (a_1) is the first term of the series,
- (r) is the common ratio of the series, and
- (n) is the number of terms.

Given (a_2 = -36) and (a_5 = 972), you can find the first term ((a_1)) and the common ratio ((r)). Then, substitute these values along with (n = 7) into the formula to find (S_7).

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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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