If f(n+2)+f(n)=0,f(0)=1,f(1)=1 find f(2009)

Asked by Gayathri devi | 11th Nov, 2010, 12:00: AM

Expert Answer:

Dear student
If f(n+2)+f(n)=0,f(0)=1,f(1)=1
then the resulting sequence will be
0,1,0,-1,0.....
Observing the pattern we have every even term is 0 and odd term is 1 or - 1 alternatively
since nth odd number is given by 2n-1 where n is a natural number
On further analysis we have 1 for all those odd numbers for which n is odd
so 2007 = 2x1004-1 so f(2007)= -1
so f(2009) will be 1
Hope it clarifies your doubt
Regards
Team Topper
 
 2007

Answered by  | 11th Nov, 2010, 12:47: PM

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