数列2:漸化式全パターン《大学受験数学》
I really wanted to re-film this lesson sooner, so please forgive me for uploading it at this late date. From next time onwards, I will upload the continuation of the functional equations course as usual. This year, I'm doing my best to make the Calculus of Limits course for Mathematics III, which I'm currently filming, ready in time for students taking the exam next year. However, since I'm basically just re-filming material from eight years ago, you can still learn from the original material without any problems. Please bear with me as I think that from now on, the recordings may become irregular, the period may be six days, or I may film at my own pace. I will do my best to avoid this as much as possible. To be honest, I haven't been able to film much recently, so my stock is slowly dwindling. Also, a word to first- and second-year high school students (although I don't think you'll be watching this class unless you're a very advanced student), I recommend that you make an effort to become proficient at formula-related proofs (derivations) during your first and second years of high school. To give some specific examples, The formula for the distance between a point and a line The sigma (Σ) formula for sequences The addition theorem for trigonometric functions Formulas for product differentiation, quotient differentiation, and composite function differentiation Differentiation formulas for trigonometric functions and exponential/logarithmic functions Derivation of the general form of quadratic curves De Moivre's theorem Properties of logarithms and formulas for changing bases Formulas for expressing components in dot products Formulas for solving quadratic equations And so on. Once students finish limit calculus, they'll be re-filmed in the order of sequences and vectors, and then probably probability, integers, quadratic curves, and the complex plane. However, it's likely that current second-year high school students will have finished sequences, vectors, and probability by the time they take their entrance exams.

Sequence 3: Simultaneous recurrence relations (University entrance exam mathematics)

A lesson on recurrence formulas that you will never forget once you hear it

Sequence 13: Handling lattice points①《University entrance exam mathematics》

The technique to solve this symmetrical equation in 30 seconds is too good to be true.

William Dunham, A tribute to Euler

England vs. DR Congo Highlights FIFA World Cup 2026 | Sportschau

イチロー、スポーツ指導者の悩み相談に持論 “怒りの感情”との向き合い方を明かす「舐めた子どもは叱る」

Belgien – Senegal Highlights | Sechzehntelfinale, FIFA WM 2026 | sportstudio

Frankreich – Schweden Highlights | Sechzehntelfinale, FIFA WM 2026 | sportstudio

Generation Military Service | Episode 1 | The First Day

数列1:いろいろな数列《大学受験数学》

Thinking process when solving integrals

A complete explanation of the congruence equation (mod) from scratch!

Sequence 9: Probability Recurrence Relations ⑥《University of Tokyo, 2012》
![[High School Mathematics] How to use King Property and its geometric meaning](https://i.ytimg.com/vi/xIvYvac4Ok8/hqdefault.jpg?sqp=-oaymwEjCNACELwBSFryq4qpAxUIARUAAAAAGAElAADIQj0AgKJDeAE=&rs=AOn4CLC9VSqf3dj8j_BM8t4fgO0dTMSH3w)
[High School Mathematics] How to use King Property and its geometric meaning

Best Explanation of Gradient, Divergence and Curl

Video: Learn to “Always” Solve Asymptotic Expressions from Zero (for beginners)
![[Attention: Reduced points] Good question with a lot of ideas and notes on the number line.](https://i.ytimg.com/vi/DAvhL3IbMy4/hqdefault.jpg?sqp=-oaymwEjCNACELwBSFryq4qpAxUIARUAAAAAGAElAADIQj0AgKJDeAE=&rs=AOn4CLBP4rUxWzFAVwVPfis3CP8F6smVyQ)
[Attention: Reduced points] Good question with a lot of ideas and notes on the number line.

