In this video I show that given that a power series with the powers 6^n is convergent, the same can't be said by a similar power series with negative powers (-6)^n which is actually divergent. First off, we can't use the radius of convergence theorem since if R = 6, we aren't given any information about the end points at x = +/- 6 which can converge or diverge. Instead, we can do a pretty clever trick by rewriting the coefficients such that we obtain an alternating series for the original series, which converges. Doing the same for our given series, we obtain a p = 1 series which is divergent, thus the answer is False. Time stamps: - Question 5: 0:00 - Solution: False: 0:18 - Radius of convergence doesn't help us: 4:03 - Modify both series by defining the coefficients: 4:26 - Original series converges by the Alternating Series Test: 5:32 - Changing coefficient for our given series: 9:31 - Our given series is a divergent p = 1 series: 12:06 Full video below: - Infinite Sequences and Series: Review and True-False Quiz: https://youtu.be/F0dsQLdXXpI - HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-review-and-true-false-quiz - Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FCqXVJv1r7eJvrvphfkr6L Related Videos: Infinite Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ . ------------------------------------------------------ Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate SUBSCRIBE via EMAIL: https://mes.fm/subscribe MES Links: https://mes.fm/links MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over another bizarre coincidence involving Donald Trump's June 14, 1946 birthday and this time show that the serial killer Jason Voorhees in the Friday the 13th movie series may actually be born on Friday the 14th, 1946. The movie character Jason Voorhees is supposedly born on the stroke of midnight on Friday June 13, 1946. But there is a major problem with this: the actual calender has June 13, 1946 on a Thursday! This, of course, means that Jason's actual birthday is on Friday the 14th, 1946 aka Trump's birthday on a blood moon! This is truly a mind-boggling coincidence and was a major reason for me making this video in the first place. Furthermore, even the original 1980 Friday the 13th movie poster has a silhouette of a person holding a bloody knife with a Full Moon in the silhouette; in other words, Blood Moon imagery. The full moon theme runs throughout the original movie. Interestingly, the 8th movie in the franchise was when June 13, 1946 was selected for Jason Voorhees. And that movie was the 1989 movie Jason Takes Manhattan; again in fitting Trump / Manhattan connection! Trump has lots of real estate in Manhattan, including a $100 million penthouse, so it's safe to say that both Jason and Trump took Manhattan! The timestamps of key parts of the video are listed below: - 1980 Horror Movie: Friday the 13th: 0:00 - Friday June 13, 1946 or Friday June 14, 1946?: 0:57 - Movie Rundown: Full Moon Theme: 3:30 - Jason Voorhees and Donald Trump Take Manhattan: 7:18 - Quora Noting that June 13, 1946 is a Thursday: 8:37 - 8th Film: Jason Takes Manhattan (1989): 11:00 - Trump's $100 million Penthouse in Manhattan: 13:09 This video was taken from my earlier video listed below: - ? Strange Coincidences Involving Donald Trump's Birthday: https://youtu.be/Yd0Ah2Komco - HIVE video notes: https://peakd.com/hive-106474/@mes/coincidences-involving-donald-trumps-birthday - Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0ElXMhiVmHKyq9IiI0SFYBk Related Videos: Full MES Occult video series: https://www.youtube.com/playlist?list=PLai3U8-WIK0EX_SJASwVeZMA-CMgu6-Ox . ------------------------------------------------------ Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate SUBSCRIBE via EMAIL: https://mes.fm/subscribe MES Links: https://mes.fm/links MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps ... https://www.youtube.com/watch?v=FOIhuc53abc

In this video I go over a list of 8 properties of vectors in terms of addition and scalar multiplication. I also provide algebraic proofs for properties 1 and 2. The remaining properties, however, are fairly straightforward and so I only briefly go over them. Property 1, a + b = b + a, be seen from the Parallelogram Law and Property 2 (called the associative law), a + (b + c) = (a + b) + c, can be proved by repeated use of the Triangle Law. The timestamps of key parts of the video are listed below: - List of 8 Vector Properties: 0:00 - Proof of Property 1: 1:39 - Proof of Property 2: 4:32 - Other Properties: 8:55 This video was taken from my earlier video listed below: - Vectors and the Geometry of Space: Vectors: https://youtu.be/0lJiVlKw4Kc - Video notes: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-vectors - Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EiRECLVkBCcFhSpbSz8XIw Related videos: Vectors and Geometry of Space video series: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over another example on Conics in Polar Coordinates and this time go over the conic given by the formula r = 10/(3 – 2cosθ). The first thing to do whenever we are given a polar equation of a conic is to re-write it in the standard conic equation form, r = e∙d/(1 – e∙cosθ). Thus in this case, we would divide by 3 on the top and bottom of the equation. Doing so we get the polar equation r = (10/3)/[1 – (2/3)cosθ]. Thus we can see that we have: eccentricity e = 2/3, the directrix x = -d = -5, and since e is less than 1, the conic is an ellipse. I also determine the vertices by setting the polar angle to 0 and π to obtain (10, 0) and (2, π) in polar coordinates. This is a very detailed video breaking down how to determine the properties and graphical illustration of a conic, so make sure to watch this video! Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIh5p9E9wPEQLA3pGr9w View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/conics-in-polar-coordinates-example-2-ellipse Related Videos: Conics in Polar Coordinates Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0H4OJpJ2gslXVLT8mP-SgJP Conic Sections Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FEUsuxP3KS5DRbidSSGBPL Polar Coordinates Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0HUFiPLsYw5_Ljd5riOUzjP Conics in Polar Coordinates: Unified Theorem: Ellipse Proof: https://youtu.be/HRFzk1vyLmg . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps