# What is the sum of the geometric series #Sigma 6(2)^n# from n=1 to 10?

The sum is

This phrase can be expressed as follows:

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The sum of the geometric series ( \Sigma 6(2)^n ) from ( n=1 ) to ( n=10 ) can be calculated using the formula for the sum of a geometric series:

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

Where:

- ( a ) is the first term of the series (in this case, ( a = 6(2)^1 = 12 ))
- ( r ) is the common ratio (in this case, ( r = 2 ))
- ( n ) is the number of terms in the series (in this case, ( n = 10 ))

Plugging the values into the formula:

[ S = \frac{12(1 - 2^{10})}{1 - 2} ]

[ S = \frac{12(1 - 1024)}{-1} ]

[ S = \frac{12(-1023)}{-1} ]

[ S = -12276 ]

So, the sum of the geometric series ( \Sigma 6(2)^n ) from ( n=1 ) to ( n=10 ) is ( -12276 ).

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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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