To find the sum of the series 3/2.5 + 3/5.8 + ... + 3/50.53, we first need to find a pattern in the denominators of the fractions.

The denominators are increasing by a constant difference of 3.3. So, the nth term in the series can be written as 3/(2.5 + (n-1)*3.3).

Now, we need to find the value of n for the last term in the series, which is 50.53. Solving for n:

2.5 + (n-1)*3.3 = 50.53
(n-1)*3.3 = 48.03
n-1 = 48.03/3.3
n-1 = 14.55
n = 15.55

Now, we can find the sum of the series using the formula for the sum of an arithmetic series:

Sum = n/2 * (first term + last term)
Sum = 15.55/2 * (3/2.5 + 3/50.53)
Sum = 7 * (1.2 + 0.0593)
Sum = 7 * 1.2593
Sum = 8.8151

Therefore, the sum of the series 3/2.5 + 3/5.8 + ... + 3/50.53 is approximately 8.8151.