if f(1)=1 and f(n+1)=2f(n)+1, if n>=1 then f(n)=

if i put some values of n then i got the answer but is there is any independent way of finding the answer.

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- Jun 1st 2011, 08:57 AMayushdadhwalhow to find the function
if f(1)=1 and f(n+1)=2f(n)+1, if n>=1 then f(n)=

if i put some values of n then i got the answer but is there is any independent way of finding the answer. - Jun 1st 2011, 09:14 AMabhishekkgp
- Jun 1st 2011, 09:19 AMTheEmptySet
I am not sure how else to solve this problem but to use the guess that the solution is of the form

If you plug this into the homogenous equation (get rid of the 1) we get

Since the nonhomogenous term is a constant we guess that the particular solution is also a constant so we have that

if we plug this in we get

So we get

Finally if we use the initial condition we get that