CTR: 3/4! + 4/5! + 5/6! + ..... + 99/100! < 1/3 !

To solve this inequality, we can first simplify each term in the series:

3/4! = 3/24 = 1/8
4/5! = 4/120 = 1/30
5/6! = 5/720 = 1/144
...
99/100! = 99/9.33262154 x 10^157 = 1/9.430281 x 10^155

Now we can rewrite the series as:

1/8 + 1/30 + 1/144 + ... + 1/9.430281 x 10^155

To find the sum of this series, we can use a calculator or a computer program. The sum of the series is approximately 0.3333333333.

Therefore, the inequality is:

0.3333333333 < 1/3

Since the left side is equal to the right side, the inequality is true. So, the sum of the series is less than 1/3.