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HSC 2013-14 MX1 Marathon (archive) (1 Viewer)

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drunkenmonkee

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Re: HSC 2013 3U Marathon Thread

2+10+60+...+(n^2 +1)n! = n(n+1)!
@n=1, lhs=rhs=2
assume true for n=k, (k^2 +1)k! = k(k+1)!
prove true fro n= k+1, k(k+1)! + (k^2 +2k+2)(k+1)! (from prev step)
= (k+1)!(k^2 +3k +2) = (k+2)(k+1)(k+1)!
RHS= (k+1)(k+2)! = (k+2)(k+1)(k+1)!
 

Sy123

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Re: HSC 2013 3U Marathon Thread

Without induction, we take the sum from 1 to n of:

 

omgiloverice

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Re: HSC 2013 3U Marathon Thread

Here is a fun question to burn off..

In this video here five men has 5 different colours of clothing to choose from, what is the probability that all the men come out wearing a different colour.
 
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