#series Trending Posts - STEMGeeks

3 months ago

SciFi Multiverse

Theorem 1 and the Test for the Divergence of Infinite Series 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

41

0

28.335 STEM

4 months ago

SciFi Multiverse

Telescoping Sum: All the terms of this series cancel out except for the first and last term 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

43

0

28.031 STEM

3 months ago

SciFi Multiverse

Theorem 2: Series of Sums is equal to Sum of Series In 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.

30

0

188.496 STEM

2 months ago

SciFi Multiverse

Exercise 2: Sum of diameters of Infinite Circles In this video, I show that the sum of diameters of an infinite number of circles contacting between two big circles sums to the radius of the bigger circles, thus providing a

28

0

11.598 STEM

3 months ago

SciFi Multiverse

Exercise 1: Sum of differences between curves y = x^n as an infinite series In this video, I show that the sum of differences between successive positive integer powers x^n for 0 ≤ x ≤ 1 can be written as an infinite series, and the resulting sum is e

44

0

208.002 STEM

2 months ago

SciFi Multiverse

Introduction to the Integral Test and Estimating Sums of Infinite Series In this video, I go over an introduction into estimating sums of series by examining whether their corresponding improper integrals converge or d

37

0

218.050 STEM

about 2 months ago

SciFi Multiverse

Estimating Sum of Series as the Midpoint is a much better Approximation than the Partial Sum In this video, I show that modifying our earlier Theorem 2 remainder estimate by adding the partial sum to both sides of the inequality pro

25

0

12.237 STEM

about 2 months ago

SciFi Multiverse

Remainder Estimate for the Integral Test + Example Remainder Estimate for the Integral Test + Example

65

0

213.539 STEM

2 months ago

SciFi Multiverse

The p-Series ∑ 1/n^p is convergent if p is greater than 1 In this video, I use the Integral Test to show that the p-series, whose terms are 1/n^p, is convergent if p is greater than 1 and divergent for all other values of p. When p is…

27

0

11.155 STEM

2 months ago

SciFi Multiverse

The Integral Test + Example on Convergence of a Series In this video, I go over the Integral Test, which states that a series converges only if its corresponding improper integral also converges. Likewise, if the improper inte

25

0

11.804 STEM