(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that Euler's constant is 0 < [tex]\gamma[/tex] < 1

2. Relevant equations

According to my book, [tex]\gamma[/tex] = lim((1+1/2+....+1/n) - log n) as n approaches infinity

3. The attempt at a solution

At first glance I was thinking about proving by contradiction.

First I assume [tex]\gamma[/tex] is equal to 0.

Then I will get lim(1+1/2+....+1/n) = lim (log n) as n approaches infinity.

However 1+1/2+....+1/n is a harmonic series which diverges, so the equality does not hold.

So [tex]\gamma[/tex] does not equal 0.

Next I assume [tex]\gamma[/tex] is less than 0.

Since log function never yields negative result, this implies that lim(1+1/2+....+1/n) < lim(log n) as n approaches infinity.

Again due to the divergent nature of harmonic series, the inequality does not hold.

These are all I have for now.

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I feel I have logic error in the attempt to solve the problem, and I hope that someone will give me a hint on the correct solution.

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# Homework Help: Need hint regarding Euler's constant question

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