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Select the correct answer.

What is the value of [tex]\sum_{i=1}^3\left(4 \times\left(\frac{1}{2}\right)^{i-1}\right)[/tex]?

A. 8
B. [tex]\frac{7}{8}[/tex]
C. 7
D. [tex]\frac{7}{2}[/tex]


Sagot :

To find the value of the sum [tex]\(\sum_{i=1}^3\left(4 \times\left(\frac{1}{2}\right)^{i-1}\right)\)[/tex], let's break it down step by step.

We need to evaluate the sum term by term.

1. For [tex]\(i = 1\)[/tex]:
[tex]\[ 4 \times \left(\frac{1}{2}\right)^{1-1} = 4 \times \left(\frac{1}{2}\right)^0 = 4 \times 1 = 4 \][/tex]

2. For [tex]\(i = 2\)[/tex]:
[tex]\[ 4 \times \left(\frac{1}{2}\right)^{2-1} = 4 \times \left(\frac{1}{2}\right)^1 = 4 \times \frac{1}{2} = 2 \][/tex]

3. For [tex]\(i = 3\)[/tex]:
[tex]\[ 4 \times \left(\frac{1}{2}\right)^{3-1} = 4 \times \left(\frac{1}{2}\right)^2 = 4 \times \frac{1}{4} = 1 \][/tex]

Now, we add these terms together:
[tex]\[ 4 + 2 + 1 = 7 \][/tex]

Thus, the value of [tex]\(\sum_{i=1}^3\left(4 \times\left(\frac{1}{2}\right)^{i-1}\right)\)[/tex] is [tex]\(7\)[/tex].

Therefore, the correct answer is:
C. 7