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Mathematical Induction

  1. Nov 2, 2008 #1
    The ’moments’ <t**n> of the distribution p(t) are defined as:

    <t**n> = integral from (0, infinity) p(t).t**n dt (1) where ** denotes to the power of

    Show (analytically) that

    <t**n> = n!τ**n (2)

    Hint: Use integration by parts to show that

    <t**n> = nτ<t**n-1> (3)

    and use mathematical induction

    I have solved the integral to get equation 3 but i can't begin to think on where to start the mathematical induction. Its been so long since i have done it.

    At first i thought that doing <tn>.<tn-1> = blabla would work but i get the answer

    blabla = nτ<t**n-1> . (n-1)τ<t**n-2>

    but i really think im missing the mark by alot.

    Sorry about the bad formatting.
  2. jcsd
  3. Nov 2, 2008 #2
    ive solved it it's fine now
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