# Thread: Question about a power series for a Calc 2 Project

1. ## Question about a power series for a Calc 2 Project

Greetings all, I'm hoping someone can point me in the right direction for this question. I'd rather not have the answer as I'd like to figure it out myself, however it might not be something that can be answered without giving it away. Well, you'll see what I mean

I have a power series:

This is basically a representation of the number of rabbits born in month n (based off of the Fibonacci numbers). The question asks me to examine this series when n is very large, and it wants to know how many rabbits are born in month n compared to month n-1.

I'm stuck here, I'm not really sure where to start or how to treat this. If anyone could provide some guidance that would be great.

2. Originally Posted by Wintaru
Greetings all, I'm hoping someone can point me in the right direction for this question. I'd rather not have the answer as I'd like to figure it out myself, however it might not be something that can be answered without giving it away. Well, you'll see what I mean

I have a power series:

This is basically a representation of the number of rabbits born in month n (based off of the Fibonacci numbers). The question asks me to examine this series when n is very large, and it wants to know how many rabbits are born in month n compared to month n-1.

I'm stuck here, I'm not really sure where to start or how to treat this. If anyone could provide some guidance that would be great.
Are you asking to sum the series?

3. Originally Posted by Wintaru
Greetings all, I'm hoping someone can point me in the right direction for this question. I'd rather not have the answer as I'd like to figure it out myself, however it might not be something that can be answered without giving it away. Well, you'll see what I mean

I have a power series:

This is basically a representation of the number of rabbits born in month n (based off of the Fibonacci numbers). The question asks me to examine this series when n is very large, and it wants to know how many rabbits are born in month n compared to month n-1.

I'm stuck here, I'm not really sure where to start or how to treat this. If anyone could provide some guidance that would be great.
Im not sure if I follow your question, the infinite power series representation is indexed over n, am I allowed to assume that n is the month 'n' ? and if so does your series represent the number of rabbits as t the time approaches infinity??

Cheers,

David

4. The month is indeed n. Maybe I miscalculated this power series. This is my work to get the equation above.

I was assuming I did this correctly. This equation is supposed to represent:

The question specifically asks us to look at a_n, when n is very large, about how many more rabbits are born in month n compared to month n-1.

Does that help at all to clarify?

5. n is only a summation index and each month will have the same sum. I believed you are confused somewhere.

6. Originally Posted by whipflip15
n is only a summation index and each month will have the same sum. I believed you are confused somewhere.
Right that n is the summation index. So your sum will give the total number of rabbits present in the population at month n. Therefore, each month will not have the same sum..right? I think...I'm rusty on power series.

7. Originally Posted by whipflip15
n is only a summation index and each month will have the same sum. I believed you are confused somewhere.
I'm afraid I don't follow. If n = 2, a_n = 3, if n = 3, a_n = 5, etc. Right?

8. To clear up all this confusion, please give us the original statement of the question.

9. Originally Posted by Wintaru
The month is indeed n. Maybe I miscalculated this power series. This is my work to get the equation above.

I was assuming I did this correctly. This equation is supposed to represent:

The question specifically asks us to look at a_n, when n is very large, about how many more rabbits are born in month n compared to month n-1.

Does that help at all to clarify?
hey mate, I noticed in your expansion of ((1/3)x)^n you have let that equal
x^n/3 which should be x^n/3^n, this may not be the area of concern but something that should be taken into consideration,

Regards,

David

ps - let me know if you need any further help

10. Originally Posted by Wintaru
I have a power series:

This is basically a representation of the number of rabbits born in month n (based off of the Fibonacci numbers).
This is what you said but what you actually mean is that $a_n$ is the number of rabbits born in month n?

11. Originally Posted by o_O
To clear up all this confusion, please give us the original statement of the question.
I'll try, there are 6 questions and this is the last. Questions 1-5 build upon each other and I was trying to avoid putting too much in the post. This is a very summarized version of the project as a whole:

Edit: By the way, I really appreciate the help everyone.

12. Originally Posted by whipflip15
This is what you said but what you actually mean is that $a_n$ is the number of rabbits born in month n?
Then if your series is correct you want to look at

$\begin{array}{c}lim\\n \rightarrow \infty \end{array}\frac{a_{n+1}}{a_n}$

13. Originally Posted by whipflip15
Then if your series is correct you want to look at

$\begin{array}{c}lim\\n \rightarrow \infty \end{array}\frac{a_{n+1}}{a_n}$
Thanks!

I actually was started in that direction, and I got this far:

Again like you said, if my series is correct (a very big IF), then this is a limit of infinity / infinity, do I then use L'Hopital's rule?

14. Ok so I went ahead and tried L'hop, this is what I came up with:

What exactly have I found here?