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#1
Apr208, 08:45 AM

P: 3

Hi,
1. The problem statement, all variables and given/known data Just having some troubles with a proof i have been asked to do, (sorry for not knowing the math code) basically, f(1)=0, f(2)=1/3 and f(n)= ((n1)/(n+1))*f(n2) and i've come up with the conjecture that f(n) = 0 when n is odd, and = 1/(n+1) when n is even. and i have to prove my conjecture, this is where i'm stuck, 2. Relevant equations anyone care to point me in the right direction? 3. The attempt at a solution not really sure what method to use, induction? 


#2
Apr208, 09:26 AM

Math
Emeritus
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Thanks
PF Gold
P: 39,691

Since you have two statements:
f(2n+1)= 0 and f(2n)= 1/(2n+1), why not try two separate induction proofs? 


#3
Apr208, 05:01 PM

P: 3

thanks for your help, "f(2n)= 1/(2n+1)" you mean 1/(n+1) right, (not being picky just making sure) yeah, i kinda what your saying, ie: 2n is a generator for all evens and 2n+1 is for odds, however, i'm not really confident on how to actually go through and do a induction proof on either, the recursive function is knda scaring me at the moment 


#4
Apr208, 05:26 PM

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P: 15,205

You are subscribed to this thread Proving conjecture for recursive function
To prove some conjecture by induction, you need to show two things:
The conjecture is obviously true for [itex]m=1[/itex] as [itex]f(2\cdot1) = 1/(2\cdot1+1) = 1/3[/itex]. All that remains is proving the recursive relationship. 


#5
Apr208, 05:31 PM

P: 3

Ahhhh, ok, thanks so much for the help! its all clicking into place now. especially after walking away from the bloody thing for a bit :P
thanks again Sam 


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