The first and the last denominator is important!

Calculus Level 2

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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