Please explain point no viii?

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Answer 1 · 2018-04-25T09:09:34

Please see the explanation below

#"^nC_r=((n),(r))=(n!)/(r!(n-r)!)#

The first term is

# S_1="^rC_r = (r!)/(r!(r-r)!) =1#

#S_1=((1+1)!)/((1+1)!(1-1)!)=1#

The first plus the second term is

#S_1+S_2= ""^rC_r +"^(r+1)C_r= 1+((r+1)!)/(r!(r+1-r)!)=r+1+1=r+2#

#S_2=((r+1+1)!)/((r+1)!(r+1-r)!)=((r+2)!)/((r+1)!(1!))=r+2#

So the result is verified.

#"^(n+1)C_(r+1) = ((n+1)!)/((r+1)!(n+1-r-1)!)=((n+1)!)/((r+1)!(n-r)!)#