Answer:
Using the formula of geometric progression, we get 5.3333333. After rounding off to the nearest hundredth or to the two digit place after the decimal, we get 5.33.
Step-by-step explanation:
Concept: Given expression means that [tex]4(\frac{1}{4} )^{n-1}[/tex] is a series that starts from n = 1 and ends at n = 10. Or we can say that the given expression is a summation from n = 1 to n = 10. This will make a geometric progression. Use the formula of geometric progression to find the answer.
[tex]4(\frac{1}{4})^{0} + 4(\frac{1}{4})^{1} + 4(\frac{1}{4})^{2} +...+ 4(\frac{1}{4})^{10}\\4\frac{-(\frac{1}{4} )^{11} +1}{-\frac{1}{4} +1} \\4\frac{1}{\frac{3}{4} } \\\frac{16}{3} \\5.33333333\\[/tex]
Now, we want the answer to the nearest hundredth. This means that the answer should have two digits after the point.
The answer, to the nearest hundredth is 5.3333333
For more explanation, refer the following link
https://brainly.com/question/27959890
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