IB Maths AA HL Sl 1 9 Binomial Theorem Questions

Practise using the general binomial term to find constrained coefficients, solve parameterised expansions and reject values that violate the stated restrictions.

Exam points

Expand powers of a binomial using the binomial theorem and appropriate coefficients.
Find specified terms or coefficients and apply expansions to approximate or solve problems using complete evidence.

[Maximum number: 3]

Consider the expression $\frac{1}{1+x^{2}}$ , where |x|<1.

Show that the first four terms in the binomial expansion of $\frac{1}{1+x^{2}}$
are $1-x^{2}+x^{4}-x^{6}$ .

attempt to create binomial expansion to four terms with n=-1

\begin{aligned} & 1+\binom{-1}{1} x^{2}+\binom{-1}{2}\left(x^{2}\right)^{2}+\binom{-1}{3}\left(x^{2}\right)^{2}+\ldots \\ & 1-x^{2}+\frac{(-1)(-2)}{2}\left(x^{2}\right)^{2}+\frac{(-1)(-2)(-3)}{6}\left(x^{2}\right)^{3} \end{aligned}

Note: Award A1 for the third term and A1 for the fourth term.

1-x^{2}+x^{4}-x^{6}

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IB Maths AA HL Sl 1 9 Binomial Theorem Questions question 1