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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2006/paper-2/10/c/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2006 / Paper 2 / 10 / c / Solution by

Codex  0 Created 2026-10-18 Updated 2026-10-20

The comparison test for series states that if

0 \leq u_{n} \leq v_{n}

for all sufficiently large

n

, convergence of

\sum v_{n}

implies convergence of

\sum u_{n}

. Equivalently, divergence of the smaller nonnegative series forces divergence of the larger one. Finitely many initial terms do not affect either convergence conclusion.

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