Pure · Sequences & series
Chapter 1 · 3
The idea
Binomial expansion for any index
Expanding (1 + x)^n and (a + bx)^n when n is negative or fractional — the series form, when it's valid, and combining it with partial fractions.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
In this lesson — start anywhere
Pure · Sequences & series
Binomial expansion for any index
Expanding (1 + x)^n and (a + bx)^n when n is negative or fractional — the series form, when it's valid, and combining it with partial fractions.
Why it works
A square root as a polynomial?
What is , without a calculator? It's — a binomial bracket with a fractional power. The old expansion can't touch it ( doesn't exist), yet the answer to three decimal places is a two-term sum: . This lesson is the machine behind that trick — the binomial expansion set free from whole-number powers, which is how calculators, physicists and approximation questions actually use it.Keep reading — free
The rest of the explanation, plus 3 worked examples you step through move by move.
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