The Harmonic Series

<p>Because the series has arbitrarily large values (D)</p> Signup and view all the answers

<p>By using the Cauchy condensation test (D)</p> Signup and view all the answers

<p>The sum of the first n terms of the harmonic series is approximately $ln(n) + \gamma$, where $ln$ is the natural logarithm and $\gamma \approx 0.577$ is the Euler–Mascheroni constant.</p> Signup and view all the answers

<p>A divergent series is a series that does not have a finite limit. In other words, the sum of the terms of the series goes to infinity.</p> Signup and view all the answers

<p>The divergence of the harmonic series was proven by Nicole Oresme in the 14th century using a precursor to the Cauchy condensation test for the convergence of infinite series.</p> Signup and view all the answers

<p>The divergence of the harmonic series can be proven by comparing the sum to an integral, according to the integral test for convergence.</p> Signup and view all the answers

<p>One application of the harmonic series is Euler's proof that there are infinitely many prime numbers.</p> Signup and view all the answers