To find the sum of the series A = 1/15 + 1/35 + ... + 1/2499, we need to first find a pattern in the denominators.

The denominators in the series are in the form of 15 + 20n, where n starts from 0. So, the nth term in the series can be written as 1/(15 + 20n).

To find the sum of the series, we need to find the value of n for which 15 + 20n = 2499.

Solving for n:
15 + 20n = 2499
20n = 2484
n = 124.2

Since n is not a whole number, we need to find the sum of the series up to the 124th term and then add the 125th term separately.

Sum of the series up to the 124th term:
S = 1/15 + 1/35 + ... + 1/2495

Using the formula for the sum of an arithmetic series:
S = n/2 * (first term + last term)
S = 124/2 * (1/15 + 1/2495)
S = 62 * (1/15 + 1/2495)
S = 62 * (166/2495)
S = 62 * 0.06653
S = 4.12

Now, we need to find the 125th term:
1/(15 + 20*124) = 1/2495

Adding the 125th term to the sum of the first 124 terms:
A = 4.12 + 1/2495
A ≈ 4.12 + 0.00040
A ≈ 4.12040

Therefore, the sum of the series A = 1/15 + 1/35 + ... + 1/2499 is approximately 4.12040.