C02 Series
对应大纲的内容
| MM2.2 | Arithmetic series, including the formula for the sum of the first $n$ natural numbers. |
| MM2.3 | The sum of a finite geometric series. The sum to infinity of a convergent geometric series, including the use of $|r| < 1$. |
学习目标
- Exploit structural symmetries by applying the invariant properties of progressions (e.g., $u_m$ $+$ $u_n$ $=$ $u_p$ $+$ $u_q$ for APs, and $u_m u_n$ $=$ $u_p u_q$ for GPs when $m$ $+$ $n$ $=$ $p$ $+$ $q$ ) to bypass tedious simultaneous equations.
- Determine series convergence rigorously by applying the strict constraint $|r|<1$ for infinite geometric series, strategically evaluating multiple valid branches (e.g., alternating sequences) when $r^2$ is derived.
- Master sigma notation $(\Sigma)$ to translate smoothly between expanded series and compact forms, efficiently applying boundary adjustments and index shifts to evaluate complex sums.
- Solve constrained progression systems by extracting initial terms $(a)$ and common differences or ratios (( $d$ or $r$ ) from non-standard conditions, strictly verifying derived parameters against contextual clues.
- Synthesise mixed progressions to solve complex problems where arithmetic and geometric sequences overlap, logically tracking changes when specific term adjustments transform one progression type into another.
建议时间
| Task | No. of Questions | Suggested Time |
|---|---|---|
| Examples | 7 | 90 min |
| Quiz | 7 | 20 min |
| Practice A | 25 | 60 min |
| Practice B | 40 | 60 min |
| Total | 79 | approx. 3-4 hrs |
Practice:
Practice:
