# How do you find the sum of the finite geometric sequence of #Sigma 2(4/3)^n# from n=0 to 15?

Sum of any geometric finite geometric series is,

substituting the values,

Symplify and get the answer.

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You can find the sum of the finite geometric sequence using the formula for the sum of a geometric series:

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

Where:

- ( S_n ) is the sum of the first ( n ) terms,
- ( a ) is the first term of the sequence,
- ( r ) is the common ratio,
- ( n ) is the number of terms.

For the given sequence ( \Sigma 2\left(\frac{4}{3}\right)^n ) from ( n = 0 ) to ( 15 ):

- ( a = 2 ) (the first term)
- ( r = \frac{4}{3} ) (the common ratio)
- ( n = 15 ) (number of terms)

Substitute these values into the formula and calculate ( S_{15} ) to find the sum of the sequence.

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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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