IB Maths AA HL 1.8 Infinite geometric series and convergence Question Bank

Practise IB Maths AA HL 1.8 by analysing convergence, parameter ranges and limiting sums in infinite geometric models.

Exam points

Derive the admissible parameter range for convergence and justify the boundary cases.
Solve a parameterised sum-to-infinity problem and select all mathematically valid values.
Evaluate the limiting behaviour of an infinite geometric model in an applied context.

[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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