#seriesUnmoderated tag#seriesHotmes in # math • 5 hr. ago • 2 min readHarmonic Series: Proving it diverges via an ingenious methodIn this video, I show that the harmonic series, 1 + 1/2 + 1/3 + 1/4 + ..., diverges by showing its even power partial sums are greater than a similar but smaller series involving repeating 1/2 terms. This is a very clever derivation, and it was due to the French scholar Nicole Oresme from the 14th century. 3Speak - YouTube - Telegram…mes in # math • 3 days ago • 2 min readTelescoping Sum: All the terms of this series cancel out except for the first and last termIn this video, I go over an infinite series in which arises an example of the famous telescoping sum such that all the terms of the series cancel except for the first and last term. The series with terms 1/(n(n+1)) is not a geometric series, so we have to start off with the definition of a convergent series and begin by writing out the terms of…mes in # math • 5 days ago • 2 min readGeometric Series: Sum of x^n series = 1/(1 - x) if |x| is less than 1Example on finding the sum of the infinite series x^n where |x| < 1 by noticing it is a convergent geometric series.mes in # math • 7 days ago • 2 min readConverting the number 2.3171717... into the fraction 1147/495 via the Geometric Series3Speak - YouTube - Telegram - Notes - Playlist - Sequences and Series - MES Links In this video, I go over an example of converting the number 2.3171717... (with infinite repeating 17) into a fraction by writing the repeating 17s as an infinite geometric series with common ratio 1/100, hence the sum is convergent.…mes in # math • 9 days ago • 2 min readExamples on Identifying Geometric Series and Determining if it Converges or Diverges3Speak - YouTube - Telegram - Notes - Playlist - Sequences and Series - MES Links In this video, I go over two examples and two methods of identifying if a series is a geometric series, and then finding its sum if it converges. In the first example, we are given the first 4 terms of a series, which we can identify the…mes in # math • 12 days ago • 2 min readGeometric Series: Deriving the Sum using an Ingenious Method (and via Similar Triangles)3Speak - YouTube - Telegram - Notes - Playlist - Sequences and Series - MES Links In this video, I go over the geometric series, which is the sum a + a r + a r^2 + ..., and show that if the absolute value of the common ratio r is less than 1, then the sum is just the first term divided by one minus the common ratio. I…mes in # math • 2 mo. ago • 2 min readDefinition and Notation of Infinite Series▶️ Watch on 3Speak - YouTube - Telegram - Summary - Hive Notes - Sections playlist - Sequences and Series playlist - MES Links In this video, I go over infinite series (or just series), which is defined as the summation of the terms of an infinite sequence of numbers. If we add an infinite sequence of numbers…humbertonic memberin Curators Community • 2 mo. ago • 6 min readREVIEW: Black Mirror - The Waldo Moment (S02E03) [ENG/ESP]🎬 Technical Details Episode: The Waldo Moment (S02E03) Series: Black Mirror Year: 2013 Director: Bryn Higgins Cast: Daniel Rigby, Chloe...
