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
