This is a pretty vague question and can be applied to many math problems not just recurrence relations.
Above I fully understand, setting up the recurrence relation from the algorithm given. And how the next step would be plugging and chugging to find a pattern that we can use.
So as shown above, we do not know what
M(n-1) is but we do know what
M(n) is equal to. So every guide just makes
M(n) -> M(n-1) by substracting
1 in the original
M(n) and then substracting
M(n-1) as well, making the new equation
M(n-1) = M((n-1)-1)+1 so now we "know" what
M(n-1) is now and can substitute it in the original equation
M(n) = M(n-1)+1 ---> M(n) = [M((n-1)-1)+1]+1
. And this is where I have my question, to me this seems like math magic just subtracting
1 inside the
M(n) parenthesis only, what substitution rule is being used here? Am I just horribly overthinking it?
9 = (4) + 5so
9-1 = (4-1)+5. I think I just answered my own question. I think doing it inside of the
M(n)and not something like
M(n)-1messed with me. $\endgroup$