Math Is Fun Forum

coolwind

Member

Registered: 2005-10-30

Posts: 30

Discrete Recursive Definition

Give a recursive definition
ex:
Cn=7n

(a)C1=7;
(b)Cn+1=Cn+7;

=====
problem:
1.Cn=n^2      2.Cn=2-(-1)^n    ????

thanks!!

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Discrete Recursive Definition

A bit hard to write that "n" in the right spot in C-sub-n ... Perhaps if you write C_n.

Anyway, I can do the first one easily:

C_n = n²

(a) C_1 = 1
(b) C_n = C_(n-1) +2(n-1) + 1

Let's check:

C_1 = 1
C_2 = 1 + 2(2-2) + 1 = 4
C_3 = 4 + 2(3-1) + 1 = 9
etc ...

---

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Discrete Recursive Definition

The second one is trickier.

Let's churn out the first few values and see how they relate to each other.

C_0 = 1
C_1 = 3
C_2 = 1
C_3 = 3
and so on.

These give differences of 2, -2, 2, -2... so we need a function of n that gives that. That can be done by using a variation of the original formula.

C_(n+1) = C_n - 2*(-1)^C_n

---

Why did the vector cross the road?
It wanted to be normal.