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

S = (n/2)(a + l)

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

In this case, the first term is 1/2 and the last term is 1/98 × 100 = 50/49.

The number of terms can be calculated by finding the common difference and using the formula:

n = (l - a) / d + 1

where d is the common difference.

The common difference can be found by subtracting the first term from the second term:

d = (1/4 - 1/2) = -1/4

Using the formula for the number of terms, we have:

n = (50/49 - 1/2) / (-1/4) + 1
= (50/49 - 49/98) / (-1/4) + 1
= (100/98 - 49/98) / (-1/4) + 1
= (51/98) / (-1/4) + 1
= (51/98) × (-4/1) + 1
= -204/98 + 1
= -102/49 + 1
= -102/49 + 49/49
= -53/49

Now we can substitute the values into the formula for the sum:

S = (-53/49 / 2)(1/2 + 50/49)
= (-53/98)(49/98 + 100/98)
= (-53/98)(149/98)
= -53(149) / (98)(98)
= -7877 / 9604

Therefore, the sum of the series 1/2×4+1/4×6+1/6×8+...+1/98×100 is -7877/9604.