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

Printable View

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

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

$\displaystyle a_0=0,a_1=2$

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

Another answer . . .

Quote:

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

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

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

Originally Posted by Soroban
Hello, cuddll1!

Another answer . . .

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

so then using n = 1
$\displaystyle a_(1+1) = a_2 = a_1 + (-1)^1 *2 = 0 + (-1)*2 = -2$
doesn't it? but doesn't $\displaystyle a_2 = 2$ and not -2
I think your solution will work with (-1)^(n+1) instead of $\displaystyle (-1)^n$
Am I right?

Thanks for everyones help! =]