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.
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