IB Maths AA HL Sl 1 8 Infinite Geometric Series Questions

Practise analysing convergence and boundary cases, solving parameterised sums to infinity and interpreting limiting behaviour in an applied geometric model.

Exam points

Determine when an infinite geometric series converges using |r| < 1.
Calculate its sum and solve for unknown parameters using complete mark-scheme evidence.

[Maximum number: 2]

The following question uses Maclaurin series to investigate approximations of mathematical constants and the accuracies of such approximations.

Given |x|<1, find the sum to infinity of the geometric series $1-x^{2}+x^{4}-x^{6}+\ldots$ .

attempt to use $S_{\infty}=\frac{u_{1}}{1-r}$

Note: Allow working with $u_{1}=1$ and $r=-x^{2}$ or $u_{1}=1-x^{2}$ and $r=x^{4}$ .

=\frac{1}{1+x^{2}}

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IB Maths AA HL Sl 1 8 Infinite Geometric Series Questions question 1