General Binomial Expansion - Subtleties (Edexcel A-Level Mathematics): Quizzes

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General Binomial Expansion - Subtleties
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For (1+ax)n(1+ax)^n, when is the binomial expansion valid?

∣ax∣<1|ax| < 1

Why does ∣x∣>1|x| > 1 cause problems in expansion 1+ax+bx2+cx3+…1 + ax + bx^2 + cx^3 + \ldots?

Powers of xx increase to infinity

For 1+8x\sqrt{1 + 8x}, what is the validity range?

∣x∣<18|x| < \frac{1}{8}

For 41−7x3\frac{4}{\sqrt[3]{1-7x}}, what is the validity range?

∣x∣<17|x| < \frac{1}{7}

What form is required to apply the binomial expansion formula?

(1+ax)n(1+ax)^n

What is the first step to expand (3+2x)−2(3+2x)^{-2}?

Factor as 3−2(1+23x)−23^{-2}(1 + \frac{2}{3}x)^{-2}

For (3+2x)−2(3+2x)^{-2}, what is the validity range?

∣x∣<32|x| < \frac{3}{2}

What are the first 3 terms of (1−2x)−12(1-2x)^{-\frac{1}{2}}?

1+x+32x21 + x + \frac{3}{2}x^2

What is the x2x^2 coefficient in x+31−2x\frac{x+3}{\sqrt{1-2x}}?

112\frac{11}{2}

When does the binomial expansion series converge?

∣x∣≤1|x| \leq 1

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