The bit I'm not totally sure on, is are you allowed to include n in the recursive definition or does it have to be solely in terms of an?
Hello sean.1986...
Here is a link to LaTeX tutorial http://www.mathhelpforum.com/math-he...-tutorial.html
here n = 1,2,3...what do you mean by "are you allowed to include n in the recursive definition"?
The definition I gave for d will compute the square of n, but I got that but looking at the definition of a square number on wiki.
"The nth square number can be calculated from the previous two by doubling the (n − 1)-th square, subtracting the (n − 2)-th square number, and adding 2, because n^2 = 2(n − 1)^2 − (n − 2)^2 + 2. For example, 2×52 − 42 + 2 = 2×25 − 16 + 2 = 50 − 16 + 2 = 36 = 62."
A recursive definition of a sequence is a rule that tells you the th term in terms of one or more proceeding terms and possibly n, and a set of initial condition sufficient to allow you to apply the recursion to calculate the subsequent terms. Such a definition is not necessarilly unique.
Lets look at (a)
now , so:
and the initial condition we need to start is that .
But we could also use two preceeding terms like:
and the initial conditions we need to start is that , and .
RonL