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Math Help - help with Induction please!

  1. #1
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    Exclamation help with Induction please!

    Suppose we are given a sequence of numbers x1, x2, x3, ,xn,
    Have the following properties: x1 = 2 and xn+1 = 2n/(n+1) xn for all n Є N

    Use Mathematical induction to prove that xn = (2^n)/n for all n Є N

    Thanks in advance
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  2. #2
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    Quote Originally Posted by lisaak View Post
    Suppose we are given a sequence of numbers x1, x2, x3, ,xn,
    Have the following properties: x1 = 2 and xn+1 = 2n/(n+1) xn for all n Є N

    Use Mathematical induction to prove that xn = (2^n)/n for all n Є N

    Thanks in advance
    Hello, lisaak,

    I assume that you know mathematical induction.

    Step 1: n = 1 so x_1=\frac{2^1}{1}=\frac{2\cdot 1}{1}=2 is true.

    step 2: Assume that x_{n}=\frac{2^n}{n} is true.

    step 3: Induction

    x_{n+1}=\frac{2n}{n+1}\cdot \frac{2^n}{n}. Rearrange:

    x_{n+1}=\frac{n}{n}\cdot \frac{2 \cdot 2^n}{n+1}=\frac{2^{n+1}}{n+1}

    EB
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