3P(n) = 1-P(n-1).

P(n) = ???

Thanks in advance.

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- Apr 19th 2009, 02:27 AMdenniszeng2008@gmail.comHow to solve this recurrence relation ?
3P(n) = 1-P(n-1).

P(n) = ???

Thanks in advance. - Apr 19th 2009, 02:47 AMCaptainBlack
- Apr 19th 2009, 05:23 AMdenniszeng2008@gmail.comComplement
it is only a recursive problem.

3P(n) = 1 - P(n-1)

3P(n-1) = 1 - P(n - 2)

...

How to figure out P(n) = ? - Apr 19th 2009, 07:38 AMaidan
- Apr 19th 2009, 07:58 AMdenniszeng2008@gmail.comBut
But i want to figure out a p(n) = n 's function but not a recurrence sequence.

- Apr 19th 2009, 08:48 AMSoroban
Hello, denniszeng!

Quote:

Subtract [2] - [1]: .

Divide by

. . Hence: .

Then is of the form: .

. . That is: . .[3]

Suppose the first term is

Then the second term is:

Substitute into [3]:

. .

Solve the system: .

Therefore: .

. . . . . . . .

- Apr 19th 2009, 05:31 PMdenniszeng2008@gmail.com
But Why P(n) can have that form relate to 1 and 1/3 ?

since it is only a special example we pick that p(n) =

Thanks very much!

I don't want to only know the solution, can you teach me how to analyze this ?

When i encounter such a problem, what should i do to figure out the right solution ?

Thanks