To find the sum of the series, we need to add up all the terms.

5/4.9 + 5/9.14 + ... + 5/44.49

First, let's find a common denominator for all the fractions. The least common multiple of the denominators is 4.9 * 9.14 * ... * 44.49.

Now, we can rewrite each fraction with the common denominator:

(5 * 9.14 * ... * 44.49) / (4.9 * 9.14 * ... * 44.49) + (5 * 4.9 * ... * 44.49) / (4.9 * 9.14 * ... * 44.49) + ... + (5 * 4.9 * 9.14 * ...) / (4.9 * 9.14 * ... * 44.49)

Now, we can add up all the numerators:

5(9.14 * ... * 44.49 + 4.9 * ... * 44.49 + ... + 4.9 * 9.14 * ...)

This sum can be simplified by factoring out a common factor of 4.9 * 9.14 * ... * 44.49:

5(4.9 * 9.14 * ... * 44.49)(1/4.9 + 1/9.14 + ... + 1/44.49)

Now, we need to calculate the sum of the reciprocals of the numbers from 4.9 to 44.49. This can be done by using a calculator or a computer program to find the sum of the series.

After calculating the sum of the reciprocals, we can multiply by 5(4.9 * 9.14 * ... * 44.49) to find the final sum of the series.