Question

pls help T^T

Answer 1

Is this a class which requires a rigours proof or more wants you to explain how it works intuitively?

Answer 2

how does it works intuituvely?

Answer 3

Think of the first few cases.
We start off with 1 pair of rabits but they have not reached maturity so we don't produce anymore rabbits
The second month (f2) we still have one pair of rabbits but now they have reached maturity so they can produce one more pair of rabbits
The third month (f3) we have 2 pairs of rabbits. The second pair has not reached maturity yet but we still have the first pair so they create another pair of rabbits.
The fourth month (f4) we have 3 pairs of rabbits and the second pair that we had before has reached maturity now. Now we have our initial pair and the second pair making new rabbits (bow chicka wow wow,. bad attempt at lighting up the mood there) meaning that we have an addition 2 pairs of rabbits.....
Do you see the pattern?

Answer 4

yeah kinda but i dont know how to express it

Answer 5

Lets look at the rabbits for some value in the series fk, can you tell me how many of the rabbit of fk are mature in terms of fk?

Answer 6

tbh idk, isit 2fk+(fk+1 - fk)

Answer 7

Thats fine, I'd just rather give you the chance :). I'm one of the guys who stubbornly insists you understand the solution :P.
Lets take a look together alright?
Notice how it takes exactly 2 months for the rabbits to reach maturity.
Also take a look at my example starting at f3
f3 saw the addition of 1 pair of rabbits
f4 saw the addition of 1 pair of rabbits
f5 will see the addition of 2 pairs of rabbits
f6 will see the addition of 3 pairs of rabbits
f7 will see the addition of 5 pairs of rabbits.....and so on and so on
Notice how the number of rabbits we are adding each month seems pretty similar to the Fibonacci sequence doesn't it?

Answer 8

why is f6 we'll see 3 pairs?

Answer 9

Let me try to help you see that for yourself by asking you another question before I tell you why. How many rabbits were alive 2 months before f6?

Answer 10

oh, i think i get it because okay after 2 months f(3), there will be 1 pair, and also f(4) because only 1 pair mature every month? so that means f(5) will have 2 pairs and in f(6) one pair of the rabbits from f(5) mature so there will be 3 pairs and so on, is that it?

Answer 11

I'm not quite sure if you have it there, small worry of mine in your explanation. Easily fixed though mind telling me how many more rabbits will be added in the next month? (f7)

Answer 12

okay, i think i'm wrong then since its not 1 pair each month.. T^T can you draw how it actually divide? im kinda confused...

Answer 13

hmmm let me try a different approach here for a second. Can you tell me how many rabbits were alive two months ago from fk? (hint its another term in the sequence)

Answer 14

2?

Answer 15

f(1)=1, f(2)=1 so 2?

Answer 16

since its pair it will be 4 rabbits total isit?

Answer 17

fk is a general term. Here lets take a look at what f actually is. If I have the xth term of f then it is the number of rabbits alive after x months from the start. Lets take a look at the fk again now.
We want the number of rabbits that were alive two months before the kth month. In other words we want he population at the kth - 2 month which we know to be f(k-2). Therefore the number of rabbits alive two months before fk is f(k-2) does that make sense?

Answer 18

f(k-2) is the subsequent months after 2 months? , what is k? woah this is depressing im so dumb ):

Answer 19

You aren't dumb, its just a misunderstanding. Don't worry I'll stay here until you get this part figured out.
Think of k as a variable. Let's take a look at k = 3 for example
then f(k-2) = f(3-2) = f1 which is the first term in the series
Now lets try k =4
f(k-2) = f(4-2) = f2 which is the second term in the series
Does that help?

Answer 20

hahah, you're so nice! (': anw , yep thts more clear, since the qn says n>= 3 so your n is actualy k. so f(1) or f(k) means the month.

Answer 21

Yeah sorry its a bit of an issue in some of my courses to write a series in terms of n then look to try and look at the "nth case", just gotten into the habit of changing it like that when looking at a particular case.

Answer 22

haha its okay, my instructor do that too. anw, how do u get how many rabbits in a month?

Answer 23

actuallt my instructor have a solution for it but i dont understand

Answer 24

hmmm I actually don't see how he came to that myself. Maybe @jim_thompson5910 might be able to see it