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Maths 2nd order homogeneous difference equations help

How did they go from step 1 to step 2.I don’t understand how they rearranged it.I understand that they were trying to make n-2 to positive n+2 and n-1 into positive n+1.

1)Pn=3/2p(n-1)+p(n-2)

2)p(n+2)-3/2p(n+1)-pn=0
(edited 4 months ago)
Reply 1
Original post by Pen48w.
How did they go from step 1 to step 2.I don’t understand how they rearranged it.I understand that they were trying to make n-2 to positive n+2 and n-1 into positive n+1.

1)Pn=3/2p(n-1)+p(n-2)

2)p(n+2)-3/2p(n+1)-pn=0

Theyve just shited n by two so
n -> n+2
n-1 -> n+1
n-2 -> n
as n is just an index, this is ok.
(edited 4 months ago)
Reply 2
Original post by mqb2766
Theyve just shited n by two so
n -> n+2
n-1 -> n+1
n-2 -> n
as n is just an index, this is ok.

Oh my goshhhh that makes sense, I tried rearranging it so many times but it didn’t make sense.Thank youuu

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