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#1 2012-11-06 02:20:34

steewan
Guest

Recurrence Relations and Backtracking

My teacher gave me this problem and I can't figure it out.

Jn= J(n-1) + n, j=2

I've gotten:
j1 = 1
j2 = 2 + 2
j3 = 2+3+2
j4 = 2+4+3+2
J5 = 2+5+4+3+2

Did I do this right so far and is if so, where do I go from here?

#2 2012-11-06 02:44:55

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,520

Re: Recurrence Relations and Backtracking

What does j=2 mean?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#3 2012-11-06 02:56:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,242

Re: Recurrence Relations and Backtracking

Hi steewan;

Every recurrence must always have an initial condition. It appears that yours is J(0)=1. In which case J(2) is incorrect.

Also you are not computing that recurrence correctly.

where do I go from here?

Depends on what you are being asked to do. Were you asked to solve the recurrence? To plot it? To determine it's limit?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#4 2012-11-06 11:12:12

scientia
Member
Registered: 2009-11-13
Posts: 222

Re: Recurrence Relations and Backtracking

steewan wrote:

My teacher gave me this problem and I can't figure it out.

Jn= J(n-1) + n, j1=2

I've gotten:
j1 = 2
j2 = 2 + 2
j3 = 2+3+2
j4 = 2+4+3+2
J5 = 2+5+4+3+2

Did I do this right so far and is if so, where do I go from here?


It's quite obvious that
. Try verifying it by mathematical induction.

Last edited by scientia (2012-11-06 11:12:49)

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