SENIOR_1.4

Date	Activities / Objectives	Images / Home work / Assignments	Remarks / Images	References / Links
Wednesday May 4 11:25 -12:05	Formal definitions and theorems about sequences Limits : Finite limits Infinite limits Limit = 0 Theorems of composition : Sum Product quotient Undecided forms : ∞ - ∞ ∞ / ∞ 0 / 0 Variations : increasing decreasing Comparisons of limits u_n ≤ v_n 0 ≤ u_n ≤ v_n v_n ≤ u_n ≤ w_n 0 ≤ \| v_n - a \| ≤ v_n Definition of Series and infinite sums	Example of applications of the definition of limits and of the comparisons theorems :		MEMO Formal definitions and theorems about sequences Example of applications
Friday May 6 11:25 -12:05	Exercises on Riemann Series : Example of Proofs of the Non Convergence of the Riemanns series of general term 1/n^a for 0 < a ≤ 1	The Harmonic Series Another Riemann's series (a=1/2)	Class of Wednesday 11th changed to Monday 9th (Exch / Liu laoshsi)
Monday May 9 9:15 -10:55	Handout of two documents : Principle of Reasonning by recurrence Initialization : P₀ True Heredidty : (P_n) => (P_n+1) Typical exercises / counter-examples : sum of the cubes Sum of the geometric series	Demo by recurrence of the formulas :		Reasonning by Recurrence Exercises of Demo by Recurrence
Friday May 13 11:25 -12:05	Handout of two documents : Theorems of Convergence of Sequences : Monotonous and bounded sequences Adjacent sequences Typical problem of convergence of a non monotonous sequence : extracted sequences of even and odd terms separately, are ADJACENT sequences		!!! NO class !!! (schedule error)	Theorems of Convergence Ex. on Adjacent Sequences (Fibonnacci Continued Fractions)
Wednesday May 18 11:25 -12:05	[Study of the two documents] Applications of the Recurrence reasonning : v_n = u_2n INcreasing w_n = u_2n+1 DEcreasing lim \|v_n - w_n\| = 0 (v_n) and (w_n) are Adjacents converge to the same limit which is the golden number	v_n = u_2n INcreasing w_n = u_2n+1 DEcreasing	TEST Friday May 25 Sequences defined by recurrence Series Limits of sequences Recurrence Reasonning applied to sequences variations and limits	Theorems of Convergence Ex. on Adjacent Sequences (Fibonnacci's Continuous Fractions)
Friday May 20 11:25 -12:05	End Study of Adjacents Sequences Study of a mixed sequence : Use of the Recurrence resasonning to prove that u_n = 4n² + 12n + 5		TEST Friday May 25 Sequences defined by recurrence Series Limits of sequences Recurrence Reasonning applied to sequences variations and limits	Exercise on Mixed Sequence
Wednesday May 22 11:25 -12:05	Review of all sequences problems in preparation of Friday's Test.	Preparation of Friday's Test.		Answers to typical Sequence problems using Recursive Reasonning
Friday May 24 11:25 -12:05	TEST Friday May 25 Sequences defined by recurrence Series Limits of sequences Recurrence Reasonning applied to sequences variations and limits		Study of a Recursive non monotonous sequence by two different methods Prove by recurrence that lim \| x_n - x \| ≤ a.qⁿ (\|q\|<1) Prove by recurrence that the two extracted sequences u_n = x_2n v_n = x_2n+1 are adjacent :	TEST A TEST B
Wednesday May 29 11:25 -12:05	Correction of Test A Comments on mistakes (u_n) INcreasing (v_n) DEcreasing lim \| u_n - v_n \| ≤ a.qⁿ Research of an approximate value of the square root of A by approaching it with the two adjacent sequences	A = 3 A = 5	TESTS RESULTS (maximum score : 40 pts) 32 ≤ N ≤ 40 := 12% 24 ≤ N ≤ 31 := 12% 16 ≤ N ≤ 23 := 21% 00 ≤ N ≤ 23 := 55%	TEST A-ANSWERS TEST A-ANSWERS