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Let:

$\displaystyle \frac{1}{50} + \frac{1}{51} + \frac{1}{52} ... + \frac{1}{98} + \frac{1}{99} = \frac{a}{b}$

Does $a$ divisible by $149$?

Hints:

Notice that $\displaystyle50+99=149$, which is as same as $a$ and $149$ is prime.

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