Question

How can you write the following expression in factorial notation?
{ ( n + 1 ) n ( n - 1 ) ( n - 2 )......( n - k + 1) } / ( n - 2 )

Answer 1

try multiplying by \(\large \dfrac{(n-k)!}{(n-k)!}\)

Answer 2

i try

Answer 3

\[\large \dfrac{ ( n + 1 ) n ( n - 1 ) ( n - 2 )\cdots( n - k + 1)(n-k)! }{ (n - 2)(n-k)! }\]

Answer 4

notice that top expression is exactly same as (n+1)! :

\[\large \dfrac{ ( n + 1 ) ! }{ (n - 2)(n-k)! }\]

Answer 5

you want to write it as a binomial coefficient is it ?

Answer 6

thank you