The first and the last denominator is important!

Calculus Level 2

Let:

150+151+152...+198+199=ab \displaystyle \frac{1}{50} + \frac{1}{51} + \frac{1}{52} ... + \frac{1}{98} + \frac{1}{99} = \frac{a}{b}

Does a a divisible by 149 149 ?

Hints:

Notice that 50+99=149 \displaystyle50+99=149 , which is as same as a a and 149 149 is prime.

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