prove \binom{n}{r}+\binom{n}{r+1}=\binom{n+1}{r+1}
shuning Member Joined Aug 23, 2008 Messages 654 Location Central Coast - Chatswood all the way :p Gender Male HSC 2009 Jul 9, 2009 #1 prove
lyounamu Reborn Joined Oct 28, 2007 Messages 9,998 Gender Male HSC N/A Jul 9, 2009 #2 shuning said: prove Click to expand... n!/((n-r)!r!) + n!/((n-r-1)!(r+1)!) = (n!(r+1))/((n-r)(n-r-1)!r!(r+1)) + (n!(n-r))/(r!(r+1)(n-r-1)!(n-r)) = (n!(n+1))/(r!(r+1)(n-r-1)!(n-r)) = (n+1)!/(r+1)!(n-r)! = (n+1)C(r+1)
shuning said: prove Click to expand... n!/((n-r)!r!) + n!/((n-r-1)!(r+1)!) = (n!(r+1))/((n-r)(n-r-1)!r!(r+1)) + (n!(n-r))/(r!(r+1)(n-r-1)!(n-r)) = (n!(n+1))/(r!(r+1)(n-r-1)!(n-r)) = (n+1)!/(r+1)!(n-r)! = (n+1)C(r+1)
shuning Member Joined Aug 23, 2008 Messages 654 Location Central Coast - Chatswood all the way :p Gender Male HSC 2009 Jul 9, 2009 #4 回复: Re: easy stuff thx man.... got 2 the last 3rd step and made an error by copying down r instead of n LOL
回复: Re: easy stuff thx man.... got 2 the last 3rd step and made an error by copying down r instead of n LOL