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Babynini
 one year ago
Find the partial sum S_n of the geometric sequence that satisfies the given conditions.
10 over sigma
k=0 beneath
3(1/2)^k on the side.
Babynini
 one year ago
Find the partial sum S_n of the geometric sequence that satisfies the given conditions. 10 over sigma k=0 beneath 3(1/2)^k on the side.

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Babynini
 one year ago
Best ResponseYou've already chosen the best response.0@jim_thompson5910 if you're available!

Empty
 one year ago
Best ResponseYou've already chosen the best response.1\[\sum_{k=0}^{10} 3 \left(\frac{1}{2} \right)^k\] Right? Any ideas how to simplify this? Do you know the geometric series formula or know how to derive it? here's the code by the way: ``` \[\sum_{k=0}^{10} 3 \left(\frac{1}{2} \right)^k\] ```

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0er they've had me using the formula s_n=a([1r^n]/[1r]) for the sum.

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0do you mean if I know how to write that out in terms?

Empty
 one year ago
Best ResponseYou've already chosen the best response.1Ok yeah that formula works, do you know what "a" and "r" and "n" are? Can you fill in the question marks? \[s_n=a \frac{1r^n}{1r}=\sum_{k=0}^{?} ?\] ``` \[s_n=a \frac{1r^n}{1r}=\sum_{k=0}^{?} ?\] ```

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0oh oh I see. \[s_n=a \frac{1r^n}{1r}=\sum_{k=0}^{n} ?\] like that?

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0\[s_n=a \frac{1r^n}{1r}=\sum_{k=0}^{n} a(r)\] is that correct? o.o

Empty
 one year ago
Best ResponseYou've already chosen the best response.1Almost not quite, since if you plug in n=1 you would get what? \[a \frac{1r^1}{1r} = 1\] for the left side and \[\sum_{k=0}^{1} a(r) = ar+ar=2ar\] on the right side. I'll give you a hint, try this, add a power of k in there: (for this example I picked 2 on the top to show how I calculate it on the right, but it also has a geometric series that I haven't shown you that it's equal to.) \[\sum_{k=0}^{2} a*r^k= ar^0+ar^1+ar^2\] But the real value on top will be n1, not n. \[a\frac{1r^n}{1r}=\sum_{k=0}^{n1} a*r^k\]

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0ah, sorry. Pc got messed up but i'm back now!

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0so what do we do for the sum formula?
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