Question
Prove that:
n!(n + 2)! = n! + (n + 1)!
n!(n + 2)! = n! + (n + 1)!
✓
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.
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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