Math Question :

f(x)=f(x-1) + f(x+1)

f(1)=1
f(2)=3

What is f(2008) ?

My answer is 4015. Do not know if it is right.

 

f(x)=f(x-1)+f(x+1)
so,f(2008)=f(2007)+f(2009)=f(2006)+f(2008)+f(2008)+f(2010)
=>f(2008)=-{(f(2010)+f(2006)}
It will grow and grow.How can anyone calculate this?
I have no clue

 

I am also confused

 

the answer is big 0, if i m wrong prove it

 

475.1090909


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f(x)=f(x-1) + f(x+1)

thus

f(1) = f(0) + f(2)

and

f(1)=1
f(2)=3

thus for f(1) = f(0) + f(2),

1 = t + 3
t = -2

and f(0) = t = -2

now we have

f(0) = -2
f(1) = 1
f(3) = 3

repeat with f(#) and by substitutions and such, we wil arrive at this +/- 1,3,2 pattern

f(-7)= -3
f(-6)= -2 (+1 from above)
f(-5)=1 (+3)
f(-4)=3 (+2)
f(-3)=2 (-1)
f(-2)=-1 (-3)
f(-1)=-3 (-2)
f(0)=-2 (+1)
f(1)=1 (+3)
f(2)=3 (+2)

now put the f(x) = #
into excel of any program into 2 columns as

-7 -3
-6 -2
-5 1

and drag at the corner or do auto continous calculation till you reach 2008 and it'll spit out 475.1091

by the way, you cant seperate out functions f(x-1) as if it is f(x) - f(1)
example: x=1
f(x-1) = x+5 ; f(0) = 6
f(x)=1, f(1)=1 but f(x-1) dont come out to be a 6 if seperated

 

The answer is 4016..
f(x)=f(x-1) + f(x+1)

f(2008) = f(2008 - 1) + f(2008 + 1)

 

lil confusing question..but i think there is no solution for this...

 

It shud be 0

 

should it be 0 ?

 

lol this is confusing

 

JessieJAmes27 was correct. 4016 is the correct answer.

 

f(x)=f(x-1) + f(x+1)

f(1)=1
f(2)=3

------------------
f(x)=f(x-1) + f(x+1)
=> f(x) = f(x)-f(1)+f(X)+f(1)
=>f(x)=2f(X)
=> 1 = 2 which is not right.

therefore,by principle of mathematical induction.. the question is wrong for all n(belongs to) N

 

f stand for "The function of" so yeah, the function of 1 equals 2, and the function of 2 equals 3, and the function of 2008 is 4016.

 

you said.. 1 equal to 2... 2 equals to 3.... so... 2008 should equal to 2009...??

 

No, we're working with functions here. If you want a pattern... The function of a number is equal .5 times the number in the function. So you would take 4016 and multiply it by .5 and get 2008. This would work for 3 and 2 as well. Proving that my calculations are correct.

 

Guys I found the answer lol. THe answer is -1

It's like this:

First try:

f(2)=3

But f(2)=f(2-1)+ f(2+1)

f(2)=f(1)+f(3)

so f(3)=f(2)-f(1)
f(3)=3-1
f(3)=2


If you keep doing this you will realize that the first 6 numbers f(1,2,3,4,5,6) will give you 1,3,2,-1,-3,-2 and it keeps repeating for every 6 numbers.

If you do 2008/6 you get a remainder of 4 which would mean the forth number which is -1

SO THE ANSWER IS -1. THanks for the help though. Thank you very much

 

are you using a book? because in my days the answers ware at the back of the book
thats how i did my hw lol

 

Your method makes no logistical sense...

 

No, it was for a competition.

Actually it makes perfect sense because it is a function = previous function + next function.

It's not like 3=1+2 or something like that, it is functions were talking here.

 

Wow, you wouldn't think I just aced a final on this or anything. I know what I was doing wrong now, lol.