To find the sum of the series 1/15 + 1/35 + ... + 1/2499, we need to find a common denominator for all the fractions.

The common denominator for 15, 35, ..., 2499 is 15 * 35 * ... * 2499. This is because each denominator is a multiple of the previous one.

So, the sum of the series can be written as:

(1/15)(35)(...)(2499) + (1/35)(15)(...)(2499) + ... + (1/2499)(15)(35)... = (1/15 + 1/35 + ... + 1/2499)(15)(35)...(2499)

Now, we can simplify the expression by canceling out the common factors:

(1/15 + 1/35 + ... + 1/2499)(15)(35)...(2499) = (1/15 + 1/35 + ... + 1/2499)(15)(35)...(2499)

Therefore, the sum of the series 1/15 + 1/35 + ... + 1/2499 is equal to 1/(15 * 35 * ... * 2499).