Maths with Lemon

Binomial extention

"I believe that the Binomial Theorem and a Bach Fugue are, in the long run, more important than all the battles of history"

James Hilton

Binomial expansion with fraction indices

What you have to know:

You must be able to manipulate simple algebraic expressions
(If not, check this lesson)
You must be able to solve simultaneous equations
(If not, check this lesson)

Key Points

1. Watch the video:

2. Read this Notes
3. Watch this video on a solved problem.

Extra

Material and references:

Hodder Book HL(ISBN: 9781510462366) :
2A

Key Points

You should be able to extend the binomial theorem to fractional and negative indices.
If \( |x| < 1 \), then for any \( n \in \mathbb{Q} \),
\[ (1 + x)^n = 1 + nx + \frac{n(n - 1)}{2!}x^2 + \frac{n(n - 1)(n - 2)}{3!}x^3 +... \]

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