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Math Help - Series

  1. #1
    Member srirahulan's Avatar
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    Arrow Series

    Prove That  |U_{n}-U_{n-1}|=\frac{1}{3^{n-1}}, for all    n\epsilon Z^{+},Where  U_{1}=1,U_{2}=2 and    U_{n}=\frac{1}{3}[U_{n-2}+2U_{n-1}] When n=3,4,5............. by using the method of Principle of Mathematical Induction. This problem, I firstly show that this case is true when n=1 and after that consider that when n=p (p\epsilon Z^{+}) the case was true but after that how can i insert (p+1) and why they give   U_{n}...please help me
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  2. #2
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    Re: Series

    Quote Originally Posted by srirahulan View Post
    Prove That  |U_{n}-U_{n-1}|=\frac{1}{3^{n-1}}, for all    n\epsilon Z^{+},Where  U_{1}=1,U_{2}=2 and    U_{n}=\frac{1}{3}[U_{n-2}+2U_{n-1}] When n=3,4,5............. by using the method of Principle of Mathematical Induction. This problem, I firstly show that this case is true when n=1 and after that consider that when n=p (p\epsilon Z^{+}) the case was true but after that how can i insert (p+1) and why they give   U_{n}...please help me
    Actually the base case is n=3.
    Assume K>3 and  |U_{K}-U_{K-1}|=\frac{1}{3^{K-1}} is true.

    Then show that  |U_{K+1}-U_{K}|=\frac{1}{3^{K}} is also true.
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