C01 Binomial Expansions
对应大纲的内容
| MM2.4 | Binomial expansion of $(1 + x)^n$ for positive integer $n$, and for expressions of the form $(a + f(x))^n$ for positive integer $n$ and simple $f(x)$.
The notations $n!$ and $\binom{n}{r}$. |
学习目标
- Apply the Binomial Theorem to expand expressions of the form $(a+b)^n$ for positive integer $n$ .
- Determine specific terms and coefficients in binomial expansions using the general term formula.
- Prove and algebraically manipulate fundamental combinatorial identities, such as symmetry and Pascal’s Identity.
- Extend binomial expansion techniques to deconstruct trinomials and track specific exponent powers within nested polynomial structures.
- Evaluate complex series sums of binomial coefficients by applying strategic value substitutions into the standard expansion.
建议时间
| Task | No. of Questions | Suggested Time |
|---|---|---|
| Examples | 10 | 90 min |
| Quiz | 7 | 30 min |
| Practice A | 20 | 40 min |
| Practice B | 20 | 60 min |
| Total | 57 | approx. 3-4 hrs |
Practice:
Practice:
