#stemUnmoderated tag#stemHotmes in # math • 9 days ago • 2 min readTheorem 2: Series of Sums is equal to Sum of SeriesIn this video, I go over Theorem 2, which states that we can move a constant out of the sum of a series as well as add or subtract series individually. These follow from the Limit Laws of Sequences, and I use this to prove that the series involving an addition of terms is equal to an addition of the individual series. I go over an example, as…mes in # math • 12 days ago • 2 min readTheorem 1 and the Test for the Divergence of Infinite SeriesIn this video, I go over Theorem 1, which states that the terms of a convergent series approach zero. Conversely, if the terms don't approach zero, the series diverges, hence providing a useful test for divergence. I prove Theorem 1 by re-arranging the n-th term as a difference of two partial sums, which, since they are convergent, are equal and…mes in # math • 14 days 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 • 17 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 • 1 mo. ago • 3 min readKepler's Second Law: A Planet's Orbit Sweeps out Equal Areas in Equal Times3Speak - YouTube - Telegram - Summary - Notes - Sections playlist - Vector Functions playlist - MES Links In this video, I derive Kepler's 2nd law of planetary motion and show that the line joining the Sun to a planet sweeps out equal areas in equal times. In other words, the rate of change of the area of the orbit…mes in # math • 1 mo. ago • 1 min readKepler’s Laws of Planetary Motion▶️ Watch on 3Speak - Odysee - BitChute - Rumble - Telegram - YouTube - PDF Notes - Summary - Notes - Sections playlist - Vector Functions playlist - MES Links In this video, I go over Johannes Kepler's three laws of planetary motion and derive them using Isaac Newton's second law of motion, F = m…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…blurt.media in # meme • 6 mo. ago • 2 min readGet paid to Blog on Blurt and Baseby @offgridlife on OGMedia View my bio on Blurt.media: Music and Math … Coffee’s cold Deadline gone Typing like a raccoon That found the “on” Got my slippers on the table And my cat on the keys Every weird thought I’m thinking Turns to digital fees [Chorus] I get paid to ramble, baby Turn my brain into a stream Blurt.blog…
