Question

show that n! (n+2)= n! + (n+1)​

Answer 1

Proof:

let RHS

= n! + (n+1)!

= n! + (n+1)*(n)(n-1)(n-2)...

= n! + (n+1)n!

= n![1+(n+1)]

= n!(n+2)

=LHS

or...

let LHS

n!(n+2)

n![(n+1)+1]

n!*(n+1)+1*n!

(n+1)!+n!

n!+(n+1)!

RHS

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