 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2016/ib/paper-1/11g/b/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-10-06

Given

ε > 0

, the Cauchy sequence property gives

N

with

d (x_{m}, x_{n}) < ε /2

for all

m, n \geq N

. Fixing

m \geq N

and letting

n \to \infty

yields

0 \leq d_{m} \leq ε /2 < ε

. Therefore

d_{m} ⟶ 0.

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