1. phi

what do you get for (1/4)^10 ? use your calculator.

2. 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

3. phi

yes

4. anonymous

5. 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 ?

6. phi

for choice C you have $960\cdot \left(\frac{1}{4}\right)^i$ when i is 1 you get $960\cdot \left(\frac{1}{4}\right)^1 \\ 960 \cdot \frac{1}{4}$