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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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  • phi
what do you get for (1/4)^10 ? use your calculator.
  • phi
1/1048576 which is roughly 1 divided by 1 million. that is a tiny number. if you keep multiplying by 1/4 you make that number even smaller and if you do that for a long time, you get 1/huge_huge_huge_number which we can call zero for all practical purposes. so eventually the terms are all so close to zero we can ignore them we use the formula \[ S = \frac{1- r^n}{1-r} \] for the sum of n terms here n is infinity which is short for "really big" r is 1/4 we know (1/4)^huge_number is so close to 0 we will use 0 and the sum is \[S= \frac{1- 0}{1-\frac{1}{4}} \] to get your final answer, multiply by 960
  • phi
yes

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@phi after this question can you please help me with mine?
  • phi
they are being tricky. they tell you the first term \(a_1= 960\) that means if you replace i with 1 in their formula, you should get 960 do you ?
  • phi
for choice C you have \[ 960\cdot \left(\frac{1}{4}\right)^i \] when i is 1 you get \[ 960\cdot \left(\frac{1}{4}\right)^1 \\ 960 \cdot \frac{1}{4} \]

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