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Rama09 [41]
3 years ago
12

Let the geometric sequence {an} be defined as follows: {12, 6, 3, 3 /2 , 3 /4 , 3/ 8 ,...} Find the sum of the entire sequence,

S∞. A) 24 B) 240 C) 1,080 Eliminate D) 2,176,782,336
Mathematics
1 answer:
Korolek [52]3 years ago
8 0

Answer:

A) 24

Step-by-step explanation:

The given geometric series is {12, 6, 3, 3 /2 , 3 /4 , 3/ 8 ,...}

Each term can be represented as a product of its previous term and \[\frac{1}{2}\]

The generic term of the series can be represented as the product of the first term 12 and \[\frac{1}{2}^{n-1}\] where n is the index of the term in the series.

The sum to infinity of such a series is given by the following formula:

\[\frac{term1}{1-ratio}\]

Substituting and calculating:

\[\frac{12}{1-\frac{1}{2}}\]

=\[\frac{12}{\frac{1}{2}}\]

=12*2 = 24

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3 0
3 years ago
Let f(x) = 8x3 − 28x + 61 and g(x) = 2x + 5. Find f of x over g of x.
antoniya [11.8K]

Answer:

4x^2-10x+11+\frac{6}{2x+5}

Step-by-step explanation:

The given functions are:

f(x)=8x^3-28x+61 and g(x)=2x+5

By algebraic properties of functions;

\frac{f(x)}{g(x)}=\frac{8x^3-28x+61}{2x+5}

We perform the long division of the two polynomials as shown in the attachment.

Therefore:

\frac{8x^3-28x+61}{2x+5}=4x^2-10x+11+\frac{6}{2x+5}

The last choice is correct

8 0
3 years ago
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kozerog [31]
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The answer is (3, 3). Hope this helped please look at others answers and check other resources as well
5 0
3 years ago
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A

Step-by-step explanation:

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