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Math Help - Find a general formula ...

  1. #1
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    Find a general formula ...

    Let x_1 = 1 and x_{n+1} = 2x_n + 1, ~ n \geq 1.

    Find and prove a general formula for x_n.


    Not sure where to start ... Do you solve for x_n ?
    Last edited by mr fantastic; September 2nd 2009 at 08:56 PM. Reason: Converted equations to latex, moved post from Adv Stats and Prob subforum (as posted, it's a difference equation problem)
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  2. #2
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    Quote Originally Posted by jaclyn91 View Post
    Let x_1 = 1 and x_{n+1} = 2x_n + 1, ~ n \geq 1.

    Find and prove a general formula for x_n.


    Not sure where to start ... Do you solve for x_n ?
    Have you been taught how to solve difference equations (recurrence relations)?
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  3. #3
    ynj
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    Quote Originally Posted by jaclyn91 View Post
    Let x_1 = 1 and x_{n+1} = 2x_n + 1, ~ n \geq 1.

    Find and prove a general formula for x_n.


    Not sure where to start ... Do you solve for x_n ?
    x_{n+1}+1=2(x_n+1)\Rightarrow x_{n}+1=2^{n-1}(x_{1}+1)
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