Show that: #nCr = n-1Cr + n-1Cr-1# ??

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Answer 1 · 2018-03-24T13:12:29

See the proof below

This is the proof of the Pascal's Triangle

#RHS=((n-1),(r))+((n-1),(r-1))#

#=((n-1)!)/((n-r-1)!(r)!)+((n-1)!)/((n-r)!(r-1)!)#

#=(n-1)!(1/((n-r-1)!(r)!)+1/((n-r)!(r-1)!))#

#=(n-1)!((n-r)/((n-r)(n-r-1)!(r)!)+r/((n-r)!r(r-1)!))#

#=(n-1)!((n-r)/((n-r)!(r)!)+r/((n-r)!(r)!))#

#=(n-1)!*n/((n-r)!(r)!)#

#=(n!)/((n-r)!(r)!)#

#=((n),(r))#

#=LHS#

#QED#