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

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

    What is the recursive definition for $\displaystyle 1 + (-1)^n $?
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  2. #2
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    Quote Originally Posted by cuddll1 View Post
    What is the recursive definition for $\displaystyle 1 + (-1)^n $?
    $\displaystyle a_0=0,a_1=2$

    $\displaystyle a_{n+2}=a_n$
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    Hello, cuddll1!

    Another answer . . .


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

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

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    Quote Originally Posted by Soroban View Post
    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?


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