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

**cuddll1** · April 6th 2008, 04:56 PM

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

**TheEmptySet** · April 6th 2008, 05:15 PM

Originally Posted by cuddll1

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

$a_0=0,a_1=2$

$a_{n+2}=a_n$

**Soroban** · April 6th 2008, 05:33 PM

Hello, cuddll1!

Another answer . . .

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

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

**cuddll1** · April 6th 2008, 05:45 PM

Originally Posted by Soroban

Hello, cuddll1!

Another answer . . .

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

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! =]

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