Question

Check my answer please

Answer 1

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

Answer 2

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

Answer 3

yes

Answer 4

@phi after this question can you please help me with mine?

Answer 5

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 ?

Answer 6

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