Answer:
5115
Step-by-step explanation:
First of all, we need to assume there is a typo involved, and that the expression is supposed to be ...
[tex]\displaystyle\sum_{i=1}^{10}{5\left(\dfrac{1}{2}\right)^i}[/tex]
The values being summed look a lot like the general term of a geometric sequence:
[tex]a_1(r^{n-1})[/tex]
The exponents in the sum range from 1 to 10, so the values being summed range from 5/2 to 5/1024. In order for that to be the case with our general term, for r = 1/2, we must have a1 = 5/2 as we let n range from 1 to 10.
The sum of the terms of the geometric sequence is ...
[tex]S_n=a_1\dfrac{1-r^n}{1-r}\\\\S_{10}=\dfrac{5}{2}\cdot\dfrac{1-\left(\dfrac{1}{2}\right)^{10}}{1-\dfrac{1}{2}}=\dfrac{5}{2}\cdot\dfrac{1023}{512}=\dfrac{5115}{1024}[/tex]
The numerator of the fraction is ...
x = 5115
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Caveat
If we have misinterpreted the intent of the problem statement, the answer will be different.
