# Mathematical Induction

1. Nov 2, 2008

### ZeroScope

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.