To solve this problem, we need to find a common denominator for all the fractions. The smallest common denominator for 2, 6, 12, ..., 72, and 90 is 180. We can convert each fraction to have a denominator of 180 and then add them together:

1/2 = 90/180
1/6 = 30/180
1/12 = 15/180
...
1/72 = 2.5/180
1/90 = 2/180

Adding these fractions together, we get:

90/180 + 30/180 + 15/180 + ... + 2.5/180 + 2/180

To simplify this expression, we can first add the numerators:

90 + 30 + 15 + ... + 2.5 + 2

Next, we can factor out a 2.5 from each term:

2.5(36 + 12 + 6 + ... + 1 + 0.8 + 0.8)

Now we can use the formula for the sum of an arithmetic series:

S = n/2(a + l)

where S is the sum of the series, n is the number of terms, a is the first term, and l is the last term.

In this case, we have:

n = 18 (there are 18 terms in the series)
a = 2.5 (the first term is 2.5)
l = 0.8 (the last term is 0.8)

Plugging these values into the formula, we get:

S = 18/2(2.5 + 0.8)
S = 18/2(3.3)
S = 18/6.6
S = 2.727...

Therefore, the sum of the series is approximately 2.727.