【京大2000】積分＆漸化式＆極限｜大学入試 数学 過去問

⭐️ "Oshie Math" allows you to ask Hayashi unlimited questions for a fixed monthly fee. You can try asking questions for free once! https://oshiemath.com/ ⭐️ "Hayashi Math Class," a specialized mathematics school where you can receive direct instruction from Hayashi. Please come for a trial lesson and interview! https://hayashi-math.com/ ✅ Official LINE for students applying to top universities: https://lin.ee/lI7n1SJ Subscriber benefits & live streams for applicants ℹ️ Shunsuke Hayashi's profile https://hayashishunsuke.com/profile/ ・Graduated from Sakae Higashi Junior High School → Chikuma High School → University of Tokyo, Faculty of Science, Department of Physics ・Scored 90% on the second-stage mathematics exam at the University of Tokyo, passing the exam as a current student ・2014 Japan Physics Olympiad Gold Medal ・Placed first place in the 2014 University of Tokyo Physics Mock Exam ℹ️ Please note ・The explanations are Shunsuke Hayashi's own and are not official university information. ・Amazon Associates links will be used when introducing books, etc. This is a problem about integral sequences from the 2000 Kyoto University Science Mathematics exam [5]. It's a complex problem in which you find a recurrence formula in (1), calculate the limit in (2), and calculate the limit of the "ratio of the difference from the limit value" in (3). It's a bit more difficult than the problems we've been dealing with recently. If you can solve this, you'll be able to pass even the University of Tokyo or Kyoto University level. This is a good question that uses a lot of knowledge from Mathematics III. Give it a try! ---------- Table of Contents 00:00 2000 Kyoto University Mathematics for Science [5] 00:39 Explanation 1: (1) Derive the recurrence formula by partial integration 05:50 Explanation 2: (2) First, roughly evaluate |cn| from the top 07:43 Explanation 3: (2) Use the result of (1) 09:22 Explanation 4: (3) Transform using the result of (1) and also use (2) 11:15 Summary: (1) Partial integration, (2) Evaluation of |cn|, (3) Using the results so far 12:47 Conclusion