Question :

Give a recursive definition (with initital condition(s) of {An} (n=1,2,3 ...)

An = (n+1)/3

I am not sure how to type "A sub n" (An) in this editor.

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- Nov 21st 2007, 05:52 PMoldguyRecursive Definition
Question :

Give a recursive definition (with initital condition(s) of {An} (n=1,2,3 ...)

An = (n+1)/3

I am not sure how to type "A sub n" (An) in this editor. - Nov 21st 2007, 08:42 PMCaptainBlack
- Nov 22nd 2007, 05:12 AMSoroban
Hello, oldguy!

Quote:

Give a recursive definition of $\displaystyle \{A_n\}$ with initial conditions.

. . $\displaystyle A_n \:=\:\frac{n+1}{3}$

. . $\displaystyle A_1 \: = \: \frac{2}{3},\;\;A_2 \:= \:\frac{3}{3},\;\;A_3 \:=\:\frac{4}{3},\;\;A_4 \:=\:\frac{5}{3},\;\;\cdots$

We see that the first term is: .$\displaystyle A_1 \:=\:\frac{2}{3}$

. . and each successive term is $\displaystyle \;\frac{1}{3}$ more than its predecessor.

Therefore: . $\displaystyle A_1 = \frac{2}{3}\;\;\text{ and }\;\;A_{n+1} \:=\:A_n + \frac{1}{3}$

- Nov 22nd 2007, 05:55 AMoldguy
Thanks, Oldguy