AHL 1.11 (HL)—Infinite geometric sequences Topic Practice
AHL 1.11 (HL)—Infinite geometric sequences Topic Practice
Students practise calculating sums of infinite geometric sequences, interpreting branching diagrams, and justifying convergence using |r| < 1.
How this is tested
- calculate total length or width using S_∞ = a/(1−r) when |r| < 1, e.g., 3/(1−2/3) = 9 cm
- justify divergence by noting |r| ≥ 1, e.g., r = 1.4 > 1 implies no finite limit to total branch length
- derive r from diagram context, e.g., r = 2 × 0.7 = 1.4 for branch multiplication factor per stage