The least value of natural number n such that `((n-1),(5))+((n-1),(6))lt((n),(r))," where"((n),(r))=(n!)/((n-r)!r!),is `

The least value of natural number n such that ((n-1),(5))+((n-1),(6))lt((n),(7))," where"((n),(r))=(n!)/((n-r)!r!),is

The least value of a natural number / such that19. The last value natural number ((n-1),(5))+((n-1),(6)) < ((n),(7)) , where ((n),(r))=(n!)/((n-r)!r!), is

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

Prove that ((n-1)!)/((n-r-1)!)+r.((n-1)!)/((n-r)!)=(n!)/((n-r)!)

If n is an even natural number , then sum_(r=0)^(n) (( -1)^(r))/(""^(n)C_(r)) equals

If n is an even natural number , then sum_(r=0)^(n) (( -1)^(r))/(""^(n)C_(r)) equals

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

Prove that (n!)/(r!(n-r)!)+(n!)/((r-1)!(n-r+1)!) =((n+1)!)/(r!(n-r+1)!)

Prove that (n!)/(r!(n-r)!)+(n!)/((r-1)!(n-r+1)!) =((n+1)!)/(r!(n-r+1)!)