On a generalisation of monotonic sequences

E. T. Copson

doi:10.1017/S0013091500009433

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A bounded monotonic sequence is convergent. Dr J. M. Whittaker recently suggested to me a generalisation of this result, that, if a bounded sequence {an} of real numbers satisfies the inequality

then it is convergent. This I was able to prove by considering the corresponding difference equation

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