For what value of n is n + 1p3 = np4

(n + 1) P 3 = (n + 1) (n) (n - 1)

n P 4 = n (n - 1) (n - 2) (n - 3) so make those equal. Both have n and (n - 1) so divide by those to cancel them out leaving

n + 1 = (n - 2) (n - 3)

n + 1 = n^2 - 5n + 6

0 = n^2 - 6n + 5

0 = (n - 1) (n - 5)

so n either = 1 or = 5. But it can't be 1 since the number before P has to be ≥ the number after.

So the only answer is n = 5