To find the value of K, we need to sum the series 10/3.5 + 10/5.7 + 10/7.9 + ... + 10/103.105.

We can rewrite the series as follows:
K = 10(1/3.5 + 1/5.7 + 1/7.9 + ... + 1/103.105)

To simplify the calculation, we can find a common denominator for all the fractions. The least common multiple of the denominators is 3.5 * 5.7 * 7.9 * ... * 103.105.

Let's calculate the value of K step by step:

1. Calculate the least common multiple (LCM) of the denominators:
LCM = 3.5 * 5.7 * 7.9 * ... * 103.105

2. Multiply each fraction by the LCM divided by its denominator:
K = 10(1/3.5 * LCM/3.5 + 1/5.7 * LCM/5.7 + 1/7.9 * LCM/7.9 + ... + 1/103.105 * LCM/103.105)

3. Simplify the expression:
K = 10(LCM/3.5 + LCM/5.7 + LCM/7.9 + ... + LCM/103.105)

4. Combine the fractions:
K = 10(LCM/3.5 + LCM/5.7 + LCM/7.9 + ... + LCM/103.105)
= 10(LCM * (1/3.5 + 1/5.7 + 1/7.9 + ... + 1/103.105))

Now, we need to calculate the LCM and evaluate the sum of the reciprocals.

Note: The calculation of the LCM and sum of reciprocals can be quite tedious, so it's recommended to use a calculator or computer program to perform these calculations.

Once you have the LCM and the sum of reciprocals, multiply them by 10 to find the value of K.