# 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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