Mathematical induction divide exercise We solve 5 exercises: 4 divides 5^n-1 6 divides 7^n-1 5 divides 11^n-6 6 divides n(n^2+5) Instagram account: https://www.instagram.com/mathphyen/ Subscribe to my channel more video lists: ################ 機率 Probability and discrete mathematics: ###################################################################### Probability interview questions: https://www.youtube.com/watch?v=qphhG_1rWf8&list=PLg9w7tItBlZtI1eM6znSYfyDEaqQtUx5b Probability theory: https://www.youtube.com/watch?v=8s-nyRLBsDo&list=PLg9w7tItBlZsvciKHBx8lXXnCtQ7Ou4cV Complex analysis: https://www.youtube.com/playlist?list=PLg9w7tItBlZsYfYG6dUISItqsSRSXaX4B Combinatorics: https://www.youtube.com/playlist?list=PLg9w7tItBlZvQt0YNfCqcULzrPme2ai7K additive combinatorics: https://www.youtube.com/playlist?list=PLg9w7tItBlZseUrmXgf_2yc2NI_obVUhB 微積分 高等微積分 代數 Calculus and advanced mathematics (abstract algebra): ###################################################################### Real analysis https://www.youtube.com/playlist?list=PLg9w7tItBlZumEJ4DacAKgstCvDHKtY63 Reduction formula in Calculus: https://www.youtube.com/playlist?list=PLg9w7tItBlZubmhgkHoHvje1uOASnkcke Integrals of trigonometric functions: https://www.youtube.com/playlist?list=PLg9w7tItBlZuwEER2YvFV06ri6i1Cj3hh (algebraic geometry)代數幾何筆記 https://www.youtube.com/playlist?list=PLg9w7tItBlZssQ4Smzgp_bk2rEszKaW0B Linear algebra Proof: https://www.youtube.com/playlist?list=PLg9w7tItBlZueH6LMeYzzwPMUlIaRhCZo 環論(ring theory): https://www.youtube.com/playlist?list=PLg9w7tItBlZs9w4wrNAuv4oJdrt-sIWUP Abstract Algebra: https://www.youtube.com/playlist?list=PLg9w7tItBlZsyZ0Ri0IDPYEwDxDXjCqB0 Group theory (群論): https://www.youtube.com/playlist?list=PLg9w7tItBlZu4Qkxz2WSk4eYZmDAC8ZY0 Galois theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZsepuNJ3tOnG238M03KrKaG 數論跟其他: number theory and others: ########### Riemann Zeta functions: https://www.youtube.com/playlist?list=PLg9w7tItBlZu4ncqL53iPd1GmwKq8yYoM Math related to pi: https://www.youtube.com/playlist?list=PLg9w7tItBlZuzFft3Y5h1LRaNvAv7ruKe Number theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZvGgPYrFxfGWaQgQBrLOOws ... https://www.youtube.com/watch?v=Eozq7cHkEYs

In this video, we just use Inequality of arithmetic and geometric means to prove that Circumradius greater than twice inradius We also showed that the equal sign happened when the equilateral triangle Instagram account: https://www.instagram.com/mathphyen/ Subscribe to my channel more video lists: ################ 機率 Probability and discrete mathematics: ###################################################################### Probability interview questions: https://www.youtube.com/watch?v=qphhG_1rWf8&list=PLg9w7tItBlZtI1eM6znSYfyDEaqQtUx5b Probability theory: https://www.youtube.com/watch?v=8s-nyRLBsDo&list=PLg9w7tItBlZsvciKHBx8lXXnCtQ7Ou4cV Complex analysis: https://www.youtube.com/playlist?list=PLg9w7tItBlZsYfYG6dUISItqsSRSXaX4B Combinatorics: https://www.youtube.com/playlist?list=PLg9w7tItBlZvQt0YNfCqcULzrPme2ai7K additive combinatorics: https://www.youtube.com/playlist?list=PLg9w7tItBlZseUrmXgf_2yc2NI_obVUhB 微積分 高等微積分 代數 Calculus and advanced mathematics (abstract algebra): ###################################################################### Real analysis https://www.youtube.com/playlist?list=PLg9w7tItBlZumEJ4DacAKgstCvDHKtY63 Reduction formula in Calculus: https://www.youtube.com/playlist?list=PLg9w7tItBlZubmhgkHoHvje1uOASnkcke Integrals of trigonometric functions: https://www.youtube.com/playlist?list=PLg9w7tItBlZuwEER2YvFV06ri6i1Cj3hh (algebraic geometry)代數幾何筆記 https://www.youtube.com/playlist?list=PLg9w7tItBlZssQ4Smzgp_bk2rEszKaW0B Linear algebra Proof: https://www.youtube.com/playlist?list=PLg9w7tItBlZueH6LMeYzzwPMUlIaRhCZo 環論(ring theory): https://www.youtube.com/playlist?list=PLg9w7tItBlZs9w4wrNAuv4oJdrt-sIWUP Abstract Algebra: https://www.youtube.com/playlist?list=PLg9w7tItBlZsyZ0Ri0IDPYEwDxDXjCqB0 Group theory (群論): https://www.youtube.com/playlist?list=PLg9w7tItBlZu4Qkxz2WSk4eYZmDAC8ZY0 Galois theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZsepuNJ3tOnG238M03KrKaG 數論跟其他: number theory and others: ########### Riemann Zeta functions: https://www.youtube.com/playlist?list=PLg9w7tItBlZu4ncqL53iPd1GmwKq8yYoM Math related to pi: https://www.youtube.com/playlist?list=PLg9w7tItBlZuzFft3Y5h1LRaNvAv7ruKe Number theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZvGgPYrFxfGWaQgQBrLOOws Set Theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZsDqBUL-CIHcVVBs9EODL_J High school math & AP calculus: https://www.youtube.com/playlist?list=PLg9w7tItBlZv165XaBIyj03q3WSMMUqDo Solving polynomial equation: https://www.youtube.com/playlist?list=PLg9w7tItBlZsheN8dz8LLPy99AaLb7_-7 ... https://www.youtube.com/watch?v=vx6r2RF4WGw

Canonical form 1: Triangular form In this video, we use mathematical induction to prove that every matrix has a Triangular form if all the eigenvalues in its field. Subscribe to my channel more video lists: exact sequences https://www.youtube.com/playlist?list=PLg9w7tItBlZuI7n7notRRA2jol69e9mc9 Ring theory lecture https://www.youtube.com/playlist?list=PLg9w7tItBlZtfPKHWGlU55kqafEgUu45u group theory lecture https://www.youtube.com/playlist?list=PLg9w7tItBlZtSHrTTVjEzAsUcO69YXY7v Category theory https://www.youtube.com/playlist?app=desktop&list=PLg9w7tItBlZtI1njDjtXt_0Hkqbn9RVvi Field theory in abstract algebra https://www.youtube.com/playlist?list=PLg9w7tItBlZtA6XhMIgIPkgj_SDKChbN- ... https://www.youtube.com/watch?v=2s4Qxqm5YIY

Algebraic geometry affine local Reduced is an affine local property algebraic geometry https://www.youtube.com/playlist?list=PLg9w7tItBlZssQ4Smzgp_bk2rEszKaW0B Donate to Channel(Support me): https://paypal.me/kuoenjui Facebook: https://www.facebook.com/mathenjui Instagram: https://www.instagram.com/mathphyen/ Advanced mathematics list: Analytic number theory: https://www.youtube.com/playlist?list=PLg9w7tItBlZu2IdPFQkrvAsPs-V2B_dxk Real analysis: https://www.youtube.com/playlist?list=PLg9w7tItBlZsaSW0zlQ7m0S3Ti51bYJg_ Group representation for finite group https://www.youtube.com/playlist?list=PLg9w7tItBlZvxk4eus_gi2Wp3yYAEXF9- exact sequences https://www.youtube.com/playlist?list=PLg9w7tItBlZuI7n7notRRA2jol69e9mc9 Ring theory lecture https://www.youtube.com/playlist?list=PLg9w7tItBlZtfPKHWGlU55kqafEgUu45u group theory lecture https://www.youtube.com/playlist?list=PLg9w7tItBlZtSHrTTVjEzAsUcO69YXY7v Category theory https://www.youtube.com/playlist?app=desktop&list=PLg9w7tItBlZtI1njDjtXt_0Hkqbn9RVvi Field theory in abstract algebra https://www.youtube.com/playlist?list=PLg9w7tItBlZtA6XhMIgIPkgj_SDKChbN- Mathematical analysis https://www.youtube.com/playlist?list=PLg9w7tItBlZu-yFYxQrWrFKcdOHRz2Fkh ... https://www.youtube.com/watch?v=LEl63S1GxWc