1.

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

Answer»

To Prove : (n+2) x (n!) + (n+1)! = (n!) x (2n + 3)

Formula : n! = n x (n-1)!

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)


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