 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ia/paper-1/12f/a/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

The series can be written as

\sum_{n = 0}^{\infty} a_{n} (z^{k})^{n} .

The original power series converges when

∣ z ∣^{k} < 2

and diverges when

∣ z ∣^{k} > 2

z

2^{1/ k} .

 New to topics? Read the docs here!