Permutations And Combinations

Question
CBSEENMA11014075

Prove that n! + (n + 1)! = [n + 2] x n !

Solution

L.H.S. = n! + (n + 1) ! = n! + [n + 1] x n! = n! [1 + n + 1] = n! (n+2)
          = [n + 2] x n! = R.H.S.
∴     L.H.S. = R.H.S.
Hence,  n! + (n + 1)! = (n + 2) x n!

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