To find the sum of the fractions 1/2 + 2/3 + 3/4 + ... + 99/100, we can rewrite each fraction with a common denominator:

1/2 = 50/100
2/3 = 66/100
3/4 = 75/100
...
99/100 = 99/100

Now, we can add up the fractions:

50/100 + 66/100 + 75/100 + ... + 99/100 = (50 + 66 + 75 + ... + 99) / 100

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

Sn = n/2 * (a1 + an)

Where n is the number of terms, a1 is the first term, and an is the last term.

Here, n = 50, a1 = 50, and an = 99. Plugging in these values:

Sn = 50/2 (50 + 99) = 25 149 = 3725

Now, we can substitute this back into the fraction sum:

3725 / 100 = 37.25

Therefore, the sum of the fractions 1/2 + 2/3 + 3/4 + ... + 99/100 is equal to 37.25.