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**coolwind****Member**- Registered: 2005-10-30
- Posts: 30

Give a recursive definition

ex:

Cn=7n

(a)C1=7;

(b)Cn+1=Cn+7;

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problem:

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

thanks!!

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,631

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

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

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.

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