Monday, 21 September 2015

discrete mathematics - Solve the following recurrence relation: an=10an2



I'm trying to solve the following recurrence equation an=10an2.



Initial conditions: a0=1, a1=10



I have tried to use characteristic polynomial and generating functions but both methods lead to contradiction.



I think I should observe Neven and Nodd as different cases but I don't know how to do it formally.




Any help would be appreciated.


Answer



We need initial values for a0 and for a1 to start with.



Notice that, a2=10a0,a4=10a2=102a0 a6=10a4=103a0



With the given initial values we get a2k=10ka0=10k



Similarly you get a2k+1=10k+1



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