Logarithme Népérien - Les Suites Numériques - 2 Bac SM - [Exercice 27]

In this video, I'll be working with you to correct a homework assignment in which we'll demonstrate some inequalities on sequences using the natural logarithm function. This video is intended for second-year baccalaureate students. Remember, it's important to try to work through the exercise before seeing the answer key. ▬▬▬▬▬▬▬ Exercise ▬▬▬▬▬▬▬ Download the exercise in Arabic here: https://cutt.ly/42cidUs Exercise: (Homework) 1) Show that (∀x∈]0,+∞[) ln⁡x≤x-1 2) Let a_1, a_2,…, a_n be strictly positive numbers Let ∶ A=1/n ∑_(k=1)^n▒a_k and u_k=a_k/A Show that ∶ ∑_(k=1)^n▒ln⁡〖u_k 〗 ≤0 then deduce that ∶ √(n&a_1 a_2…a_n )≤1/n ∑_(k=1)^n▒a_k 3) Application∶ Show that ∶(∀x≥0) x^n/(1+x+x^2+⋯+x^2n )≤1/(2n+1) 4) Show that ∶(∀n∈N* ) 1/n+1/(n+1)+⋯+1/2n≥2/3 00:22 Exercise statement 01:16 Question 1) 04:08 Question 2) 13:07 Question 3) 22:38 Question 4) ▬▬▬▬▬▬▬ SUBSCRIBE ▬▬▬▬▬▬▬ 💡👉 Subscribe here:    / @mathphys   ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ 🔔 Please click the LIKE button if you enjoy our content, leave a comment, and subscribe to our YouTube channel to receive our new videos. 👉Leave me your questions in the comments section if you don't understand something! 😀 💡Please also remember to SHARE with your friends!!💪💪🔥🔥 ▬▬▬▬▬▬▬▬▬SOCIAL MEDIA▬▬▬▬▬▬▬▬▬▬   / 536279063660093     / math-phys-112225370317476     / math.phys   ▬▬▬▬▬▬▬ SIMILAR VIDEOS ▬▬▬▬▬▬▬ Natural Logarithm - Numerical Sequences - 2 Baccalaureate Mathematics - [Exercise 27]:    • Logarithme Népérien - Les Suites Numérique...   Function Study - Numerical Sequences - Natural Logarithm - 2 Baccalaureate Mathematics - [Exercise 31]:    • Etude de Fonction – Suites Numérique - Log...   Natural Logarithm - Implicit Sequences - 2 Baccalaureate Mathematics - [Exercise 26]:    • Logarithme Népérien - Suites Implicites - ...   Function Study - Integral Calculus - S.Exp Practice Exam - [Exercise 26]:    • Etude de Fonction - Calcul Intégral - Exam...   Natural Logarithm - Implicit Sequences - 2 Baccalaureate Mathematics - [Exercise 21]:    • Logarithme Népérien - Suites Implicites - ...   Natural Logarithm - Implicit Sequences - 2 Baccalaureate (Science and Mathematics) - [Exercise 20]:    • Logarithme Népérien - Suites Implicites - ...   2021 National Exam (Science and Mathematics) - Function Study - Natural Logarithm - Implicit Sequences - 2:    • Examen National 2021 SM - Etude de Fonctio...   2021 National Exam (Science and Mathematics) - Function Study - Natural Logarithm - Implicit Sequences:    • Examen National 2021 SM - Etude de Fonctio...   Natural Logarithm Function - Limit of Natural Logarithm - 2 Baccalaureate (Science and Mathematics) - [Exercise 18]:    • Fonction Logarithme Népérien - Limite Loga...   Natural Logarithm - Solving an Inequality - 2 Baccalaureate (Science and Mathematics) - [Exercise 17]:    • Logarithme Népérien - Résoudre une Inéquat...   Limit of a Sum - Natural Logarithm - 2nd Baccalaureate (Science and Mathematics) - [Exercise 15]:    • Limite d'une Somme - Logarithme Népérien -...   Limit of a Sum - Numerical Sequences - 2nd Baccalaureate (Science and Mathematics) - [Exercise 14]:    • Limite d'une somme - les Suites Numériques...   2021 National Exam (Science and Mathematics) - Function Study - Numerical Sequences:    • Examen National 2021 SM - Etude de Fonctio...   Implicit Sequence - Function Study - Natural Logarithm - Practice Exam (Science and Mathematics) [Exercise 9]:    • Suite Implicite - Etude de Fonction - Loga...   Implicit Sequence - Function Study - Natural Logarithm - 2014 National Exam (Science and Mathematics)    • Suite Implicite - Etude de Fonction - Loga...   Natural Logarithm - Implicit Sequence - 2020 National Exam (SM) Make-up - [Exercise 14]:    • Logarithme Népérien - Suite Implicite - Ex...   Function Study - Natural Logarithm - 2020 National Exam (SM) - [Exercise 9]:    • Etude de Fonction - Logarithme Népérien - ...   Natural Logarithm - Natural Logarithm Function - Course Review - 2nd Baccalaureate (SM) (S.ex):    • Logarithme Népérien - Fonction Logarithme ...   ▬ ... Sciences Bac Biof Bac Sciences Math Mathematical Sciences Terminal National Exam ▬▬▬▬▬▬▬▬▬▬ Video Recap ▬▬▬▬▬▬▬▬▬ • We will demonstrate some inequalities on sequences and sums using the properties of the natural logarithm function. • Finite Increment Theorem (FAT). • Telescopic Sum 👉 And you can check out the other videos in this playlist to see other exercises on natural logarithm functions and numerical sequences with their applications. YouTube has become a veritable math site (math fr) for science and science ex students, where there are math courses, online math. In this video, we will focus on the math course on limits. ▬▬▬▬▬▬▬▬ KEYWORDS ▬▬▬▬▬▬▬▬ #homework #Natural_Logarithm #TAF