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Math Help - Mathematical Induction Problem

  1. #1
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    Mathematical Induction Problem

    Ok guys, I really need help with this, I can understand almost everything in my class except induction. Can someone please help me with a solution to the following problem?

    Use mathematical induction to show that

    F(n) = 3  2^{n-1}\ -2

    is the solution for the recurrence relation:

    T(n) = 2T(n1) + 2 for n > 1 and T(1) = 1

    Thanks in advance for any help supplied.
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  2. #2
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    Quote Originally Posted by Kostapoulous View Post
    Ok guys, I really need help with this, I can understand almost everything in my class except induction. Can someone please help me with a solution to the following problem?

    Use mathematical induction to show that

    F(n) = 3  2^{n-1}\ -2

    is the solution for the recurrence relation:

    T(n) = 2T(n1) + 2 for n > 1 and T(1) = 1

    Thanks in advance for any help supplied.
    P(k) is

    F(k)=(3)2^{k-1}-2


    P(k+1) is

    F(k+1)=(3)2^k-2


    Try to show that P(k) "being true" forces P(k+1) to also be true.

    F(k+1)=[2]F(k)+2

    which, if P(k) is true, is

    2\left[(3)2^{k-1}-2\right]+2=(3)2^k-4+2=(3)2^k-2

    Have a shot at the base case.
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