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Permutations — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSPermutations3 Marks
Question
Prove that: n!(n + 2)! = n! + (n + 1)!
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Answer

We have, L.H.S. = n! + (n + 1)! = n! + (n + 1)(n + 1 - 1)! = n! + (1 + n + 1) = n!(n + 2) = R.H.S. $\therefore$ n!(n + 2)! = n! + (n + 1)! Hence, proved.

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