Hundred Fractions is More Than Enough

Python 2.7:

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from fractions import Fraction as frac
def odds_gen():
    yield 1
    n = 3
    while True:
        yield n
        yield n
        n += 2
def evens_gen():
    n = 2
    while True:
        yield n
        yield n
        n += 2
odds = odds_gen()
evens = evens_gen()
total = 0
for i in xrange(100):
    total += frac(next(evens),next(odds))
print total.numerator+total.denominator

$\frac{2}{1}+\left(\frac{2}{3}+\frac{4}{3}\right) +\left(\frac{4}{5}+\frac{6}{5}\right)+\left(\frac{6}{7}+\frac{8}{7}\right)+\ldots+\left(\frac{98}{99}+\frac{100}{99}\right)+\frac{100}{101}\\=2+49\times{2}+\frac{100}{101}=100+\frac{100}{101}=~\frac{10200}{101}$ .

Thus, the required answer is $~~10200+101=\boxed{10301}$