To solve this inequality, we need to find a common denominator for all the fractions and then add them up.

First, let's express all the fractions with a common denominator of 105:

2/15 = 14/105
2/35 = 6/105
2/56 = 3/105
...
2/9999 = 2/105

Now, we can rewrite the inequality as:

14/105 + 6/105 + 3/105 + ... + 2/105 < 1/3

Combining all the fractions, we get:

(14 + 6 + 3 + ... + 2) / 105 < 1/3
(2 + 3 + 4 + ... + 9999) / 105 < 1/3

Now, we need to find the sum of the numbers from 2 to 9999:

Sum = (9999 * (9999 + 1)) / 2 - 1
Sum = 49995000

Now, we can substitute the sum back into the inequality:

49995000 / 105 < 1/3
476142.857 < 1/3

Since 476142.857 is less than 1/3, the inequality holds true. Therefore, the sum of the fractions is less than 1/3.