In 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

Tutorial on a convergence theorem for infinite series, and what follows from it is the Test for Divergence.

In 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

In 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 telescoping sum

Example of a series whose sum can be determined by using the telescoping sum and partial fraction decomposition.

In this video, I show that the infinite series xn = x0 + x1 + x2 + ... is just a geometric series, and converges if the absolute value of x is less than 1. By common convention, x0 = 1, so the first term

Example on finding the sum of the infinite series x^n where |x| < 1 by noticing it is a convergent geometric series.

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,

Example on converting a number with repeating digits into a fraction of integers via the geometric series.

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

Two examples on identifying geometric series and finding their sums, if the series converges.

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

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

YouTube - Rumble - Odysee - BitChute - X - Twitch - Math Q/A playlist Electromagnetic potentials are mathematical fields introduced via vector calculus identities to satisfy the homogeneous Maxwell equations

3Speak - YouTube - Telegram - Notes - Playlist - Vector Functions - MES Links In this video, I use the equation for Kepler's third law to calculate the required altitude above Earth's equator of a satellite

In this video, I use Kepler's third law to calculate the length of Earth's elliptical orbit to be around 299,000,000 km wide and takes about 365.25 days to complete 1 full revolution. The equation for

3Speak - YouTube - Telegram - Summary - Notes - Sections playlist - Vector Functions playlist - MES Links In this video, I use Kepler's third law to calculate the length of Earth's elliptical orbit to

In this video, I derive Kepler's 3rd Law of planetary motion and obtain a formula for a planet's period of orbit around the Sun in terms of the length of its major axis. Using the results of Laws 1 and

3Speak - YouTube - Telegram - Summary - Notes - Sections playlist - Vector Functions playlist - MES Links In this video, I derive Kepler's 3rd Law of planetary motion and obtain a formula for a planet's

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