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Need help! Is there a quick technique?

I encountered the following question. You can brute-force the calculation, but I'm curious to know if there is an easy rule or intuition that I'm missing....

Which is bigger,

100000001/100000002 or
200000001/200000002

2 weeks, 1 day ago

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Hint: If $$a > b> 0$$, then $$\dfrac1a < \dfrac 1b$$, and also $$1 - \dfrac1a > 1 - \dfrac 1b$$.

- 1 week, 5 days ago

They are both slightly less than 1. Which is closer to 1?

- 2 weeks, 1 day ago

That's the question!

- 2 weeks, 1 day ago

If we want to see which is closer to 1, we should compare $1 - \frac{100000001}{100000002} \quad \text{and} \quad 1 - \frac{200000001}{200000002}.$ What does that give you?

- 2 weeks, 1 day ago