# How do you find #S_n# for the geometric series #a_1=4#, r=0.5, n=8?

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To find ( S_n ) for the geometric series with ( a_1 = 4 ), ( r = 0.5 ), and ( n = 8 ), you use the formula:

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

Substitute the given values:

[ S_8 = 4 \frac{{1 - 0.5^8}}{{1 - 0.5}} ]

[ S_8 = 4 \frac{{1 - 0.00390625}}{{1 - 0.5}} ]

[ S_8 = 4 \frac{{0.99609375}}{{0.5}} ]

[ S_8 = 4 \times 1.9921875 ]

[ S_8 = 7.96875 ]

So, ( S_8 = 7.96875 ).

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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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