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Could someone find a proof other than induction for these two equations?
1) nC1+2(n-1)*(nC2)+3(n-1)^2*(nC3)+...+n(n-1)^(n-1)*(nCn) = n^n
where n in N and n >= 2
2) Sum (from 3 to n) [3Pk*nCk] =(3Pn)*2^(n-3)
by the way, 3Pk is k!/(k-3)! some ppl like to write kP3
Is this a typo?Quote:
Originally posted by bugzpodder
nC1+2(n-1)*(nC2)+3(n-1)^2*(nC3)+...+n(n-1)^(n-1)*(nCn) = n^n
I may be wrong but are you sure the formula should not begin with "1" instead of "n"? i.e.
C1+2(n-1)*(nC2)+3(n-1)^2*(nC3)+...+n(n-1)^(n-1)*(nCn) = n^n
looks fine to me! nCk=n choose k=n!/[(n-k)!k!]
Right, I was misled probably because the first C term was not enclosed within parenthesis and after 8 hours work my brain is somewhat overheated.
Just wanted to make sure before I tried my luck on this one.