There are 100 fractions in the following set.

$$ \Big\lbrace \frac{1}{4}, \frac{4}{7}, \frac{7}{10}, \frac{10}{13}, ... , \frac{292}{295}, \frac{295}{298}, \frac{298}{301} \Big\rbrace $$

Each fraction after the first is found by adding 3 to the preceding fraction's numerator and denominator. What is the product of these 100 fractions?

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$$ \Big\lbrace \frac{1}{\cancel{4}}, \frac{\cancel{4}}{\cancel{7}}, \frac{\cancel{7}}{\cancel{10}}, \frac{\cancel{10}}{\cancel{13}}, ... , \frac{\cancel{292}}{\cancel{295}}, \frac{\cancel{295}}{\cancel{298}}, \frac{\cancel{298}}{301} \Big\rbrace $$

Notice that every factor cancels out except the first \(1\) and the last \(301\).