Determine the first four terms of the sequence in which the nth term is a_n=(n+1)!/(n+2)!

Answer 1

To find the first four terms of the sequence, we need to substitute values for n into the given expression for a_n.

When n = 1:
a_1 = (1+1)! / (1+2)! = 2! / 3! = 2/6 = 1/3

When n = 2:
a_2 = (2+1)! / (2+2)! = 3! / 4! = 6/24 = 1/4

When n = 3:
a_3 = (3+1)! / (3+2)! = 4! / 5! = 24/120 = 1/5

When n = 4:
a_4 = (4+1)! / (4+2)! = 5! / 6! = 120/720 = 1/6

Therefore, the first four terms of the sequence are:
1/3, 1/4, 1/5, 1/6.