1
vote
1answer
58 views

Establishing formula from recurrence

Can anyone tell me how do we establish a formula from a given recurrence relation? Take the example of $f(n) = 2f(n-1) + 1$, $n \in \mathbb{Z^+}$, $f(1) = 1$ When I write out the first few values, it ...
3
votes
3answers
53 views

How to get from $1 + (-1)^{n+1}$ to $1 + [((−1)^{n }) − 1] (−1)$

I need some help with the algebra here. I have the following explanation, and I really can't follow the algebra. Could you also maybe give me some tips on how to think about such problems. $a_n = 1 ...
0
votes
1answer
113 views

Convert a recurrence relationship into an algebraic equation

I have a piece of code that describes a recursive relationship to produce a logarithmic sweep: ...