# Thread: Help - Geometric Series.

1. ## Help - Geometric Series.

Hi,
I just found this site, looks like a great place. I'm looking for some help regarding a question in one of my assignments, I can't seem to figure it out with my material at hand.

http://img178.imageshack.us/img178/8941/img5274pb5.jpg
That is the problem in question.
Now the problem is that I don't even know where to begin. If someone could just give me a hand in understanding what needs to be done to solve it that would be fantastic, I've been melting my brain trying to solve it. I'm sure the solution is quite simple, a few times I've ended up with k=1 being an answer, but I couldn't seem to prove that once I was finished.

2. Originally Posted by Fishsticks
Hi,
I just found this site, looks like a great place. I'm looking for some help regarding a question in one of my assignments, I can't seem to figure it out with my material at hand.

http://img178.imageshack.us/img178/8941/img5274pb5.jpg
That is the problem in question.
Now the problem is that I don't even know where to begin. If someone could just give me a hand in understanding what needs to be done to solve it that would be fantastic, I've been melting my brain trying to solve it. I'm sure the solution is quite simple, a few times I've ended up with k=1 being an answer, but I couldn't seem to prove that once I was finished.
The question is asking you to find the largest $k$ such that:

$100 \left( \frac{11}{17} \right)^{k-1}-50 \left( \frac{14}{17} \right)^{k-1}>14$

RonL

3. Thank you for your help, I however still can't figure out how to solve it.

It may be asking a bit much, but could you walk me through solving it so I can better understand what was required? Thanks.

4. Originally Posted by CaptainBlack
The question is asking you to find the largest $k$ such that:

$100 \left( \frac{11}{17} \right)^{k-1}-50 \left( \frac{14}{17} \right)^{k-1}>14$

RonL
Originally Posted by Fishsticks
Thank you for your help, I however still can't figure out how to solve it.

It may be asking a bit much, but could you walk me through solving it so I can better understand what was required? Thanks.
You start with $k=1$ and check if:

$100 \left( \frac{11}{17} \right)^{k-1}-50 \left( \frac{14}{17} \right)^{k-1}>14$

if so try $k=2$, ..

Being lazy I automate this as in the code fragment below, to find the required $k$ is $2$.

Code:
>
>k=[1:5]
Column 1 to 3:
1             2             3
Column 4 to 5:
4             5
>
>100*(11/17)^(k-1)-50*(14/17)^(k-1)
Column 1 to 3:
50       23.5294       7.95848
Column 4 to 5:
-0.834521      -5.46809
>

RonL