Proving <t**n> = n!τ**n using Mathematical Induction

[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 I am missing the mark by a lot.

Sorry about the bad formatting.

 

[ZeroScope]

ive solved it it's fine now