# $$\dfrac{1}{2017}$$

The $$a_1, a_2, \dots, a_{2017}$$ are $$2017$$ distinct odd positive integers. Is it possible that

a) $$\dfrac{1}{a_1}+\dfrac{1}{a_2}+\dots+\dfrac{1}{a_{2017}}=\dfrac{2017}{10}$$?

b) $$\dfrac{1}{a_1}+\dfrac{1}{a_2}+\dots+\dfrac{1}{a_{2017}}=\dfrac{2017}{100}$$?

Note by Áron Bán-Szabó
1 year ago

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Neither sum is possible.

The highest sum you can get would be by summing the reciprocals of the 2017 lowest odd positive integers. That gives a bit more than 4.44, so not even close to 2017/100.

I think if you kept going, you could get as large a sum as you desired though....

- 1 year ago

What do you mean by "2,017" and "20,17"?

- 1 year ago

I corrected it, now you know What I mean, I hope.

- 1 year ago