# Prove that 1 + 1.

To Prove: 1 + 1. 1P1 + 2. 2P2 + 3. 3P3 + …. n. nPn = n+1Pn+1.

Formula Used:

Total number of ways in which n objects can be arranged in r places (Such that no object is replaced) is given by,

nPr

1 + 1. 1P1 + 2. 2P2 + 3. 3P3 + …. n. nPn = n+1Pn+1.

1 + (2! - 1!) + (3! - 2!) + (4! - 3!) + …….((n + 1)! - n!) = (n + 1)!

1 + ((n + 1)! - 1!) = (n + 1)!

(n + 1)! = (n + 1)!

Hence proved.

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