https://blog.dlow.me/tags/proof-without-words/Recent content in Proof-Without-Words on dlow's blogHugoen-usThu, 16 Jul 2020 09:44:46 +0100https://blog.dlow.me/maths/harmonic-mean/Thu, 16 Jul 2020 09:44:46 +0100https://blog.dlow.me/maths/harmonic-mean/<p>These are some notes on harmonic mean taken some time in 2016.</p> <h1 id="harmonic-mean">Harmonic mean <a class="anchor" href="#harmonic-mean"><span></span></a></h1><p>We start by introducing three number sequences:</p> <ul> <li>An Arithmetic Progression (AP) is given by $a$, $a + d$, $a + 2d$, &hellip;</li> <li>A Geometric Progression (GP) is given by $a$, $ar$, $ar^2$, &hellip;</li> <li>A Harmonic Progression (HP) is given by $\{1/a_i\}$ where $\{a_i\}$ is an AP.</li> </ul> <p>Given a number sequence, we can define its mean. We use two here for simplicity.</p>