Prove that (n + 2) × (n!) + (n + 1) ! = (n!). (2n + 3)

Question

Philoid · Accepted Answer

To Prove :

Formula :

L.H.S. = (n + 2) × (n!) + (n + 1)!

= (n + 2) × (n!) + (n + 1) × (n!)

= (n!) × [(n + 2) + (n + 1)]

= (n!) × (2n + 3)

= R.H.S.

∴L.H.S. = R.H.S.

Conclusion : (n + 2) × (n!) + (n + 1)! = (n!) × (2n + 3)