To prove that the given expression is less than 1, we can simplify each term and add them up.

1/1! = 1/1 = 1
1/2! = 1/2 = 0.5
1/3! = 1/6 ≈ 0.1667
1/4! = 1/24 ≈ 0.0417
1/5! = 1/120 ≈ 0.0083

Now, let's add up these values:

1 + 0.5 + 0.1667 + 0.0417 + 0.0083 = 1.7167

Since 1.7167 is greater than 1, we can conclude that:

1/1! + 1/2! + 1/3! + 1/4! + 1/5! < 1

Therefore, the given expression is indeed less than 1.