To find the value of A, we need to evaluate the sum of the given series.

The given series is:

A = 1/1.2 + 1/3.4 + 1/5.6 + ... + 1/49.50

We can rewrite each term in the series as:

1/1.2 = 5/6
1/3.4 = 10/17
1/5.6 = 25/42
...
1/49.50 = 100/165

So, the series can be written as:

A = (5/6) + (10/17) + (25/42) + ... + (100/165)

To simplify the series, we need to find a common denominator for all the terms. The least common multiple (LCM) of 6, 17, 42, and 165 is 2,730.

Multiplying each term by the appropriate factor to get the common denominator, we have:

A = (5/6) * (455/455) + (10/17) * (160/160) + (25/42) * (65/65) + ... + (100/165) * (26/26)

Simplifying each term, we get:

A = 2275/2730 + 1600/2730 + 1625/2730 + ... + 2600/2730

Now, we can add all the terms together:

A = (2275 + 1600 + 1625 + ... + 2600) / 2730

To find the sum of the arithmetic series, we can use the formula:

Sum = (n/2) * (first term + last term)

In this case, the first term is 2275 and the last term is 2600. The number of terms, n, can be found by dividing the difference between the last term and the first term by the common difference (which is 25 in this case) and adding 1.

n = (2600 - 2275) / 25 + 1 = 13

Substituting the values into the formula, we have:

A = (13/2) * (2275 + 2600) / 2730

Simplifying further:

A = (13/2) * (4875) / 2730

A = 13 * 4875 / (2 * 2730)

A = 63,375 / 5460

A ≈ 11.6

Therefore, the value of A is approximately 11.6.