# How do you find the sum of the finite geometric sequence of #Sigma 8(-1/2)^i# from i=0 to 25?

See below.

The sum of a geometric series is given by:

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To find the sum of the finite geometric sequence ( \sum_{i=0}^{25} 8 \left( -\frac{1}{2} \right)^i ), you can use the formula for the sum of a finite geometric series:

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

Where:

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

For the given sequence:

- ( a = 8 )
- ( r = -\frac{1}{2} )
- ( n = 26 )

Plug these values into the formula:

[ S = \frac{8(1 - (-\frac{1}{2})^{26})}{1 - (-\frac{1}{2})} ]

[ S = \frac{8(1 - \frac{1}{2^{26}})}{1 + \frac{1}{2}} ]

[ S = \frac{8(1 - \frac{1}{67108864})}{\frac{3}{2}} ]

[ S = \frac{8 \times 67108863}{3} ]

[ S = 178956970.67 ]

So, the sum of the given geometric sequence is approximately ( 178956970.67 ).

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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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