Question: Consider the third order difference equation a n +3 = a n +2 + a n +1 + a n where a 0 = a

Consider the third order difference equation

an+3= an+2+ an+1+ an

where

a0= a1= 0 and a2 = 1.

What is the limit

lim +1/

That is, asn increases without bound, what does this ratio of consecutive terms approach? Nearest 0.01.

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