# What is the recursive definition for 1 + (-1)^n?

• April 6th 2008, 04:56 PM
cuddll1
What is the recursive definition for 1 + (-1)^n?
What is the recursive definition for $1 + (-1)^n$?
• April 6th 2008, 05:15 PM
TheEmptySet
Quote:

Originally Posted by cuddll1
What is the recursive definition for $1 + (-1)^n$?

$a_0=0,a_1=2$

$a_{n+2}=a_n$
• April 6th 2008, 05:33 PM
Soroban
Hello, cuddll1!

Quote:

What is the recursive definition for: . $1 + (-1)^n$ ?

. . $a_{n+1} \;=\;a_n + (-1)^n\!\cdot\!2$

• April 6th 2008, 05:45 PM
cuddll1
Quote:

Originally Posted by Soroban
Hello, cuddll1!

. . $a_{n+1} \;=\;a_n + (-1)^n\!\cdot\!2$

so then using n = 1
$
a_(1+1) = a_2
= a_1 + (-1)^1 *2
= 0 + (-1)*2
= -2
$

doesn't it? but doesn't $a_2 = 2$ and not -2
I think your solution will work with (-1)^(n+1) instead of $(-1)^n$
Am I right?

Thanks for everyones help! =]