Paper 1, Section I, D

Analysis I | Part IA, 2016

What does it mean to say that a sequence of real numbers (xn)\left(x_{n}\right) converges to xx ? Suppose that (xn)\left(x_{n}\right) converges to xx. Show that the sequence (yn)\left(y_{n}\right) given by

yn=1ni=1nxiy_{n}=\frac{1}{n} \sum_{i=1}^{n} x_{i}

also converges to xx.

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