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Incoming links: Telescoping increment lemma
Past exam of the mathematics course of the University of Cambridge 2024 ia Paper 1 11E b Solution Created 2026-09-24 Updated 2026-09-25
Define the continuous functionAt the mesh points its values telescope:If one term is zero, the result follows immediately. Otherwise the terms cannot all have the same sign, so there are mesh points at which is positive and negative. The intermediate value theorem between those points gives an with . Thus the telescoping increment lemma yields