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

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- Apr 6th 2008, 04:56 PMcuddll1What is the recursive definition for 1 + (-1)^n?
What is the recursive definition for $\displaystyle 1 + (-1)^n $?

- Apr 6th 2008, 05:15 PMTheEmptySet
- Apr 6th 2008, 05:33 PMSoroban
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 PMcuddll1
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! =]