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- W2382036710 abstract "This article discusses a number of functions-square root function of the arithmetic mean and the geometric mean of the limits of the problem,which is the distribution with the square root function value is closely related.Let n be a positive integer,a2(n) be the smallest square root greater than or equal to n,and b2(n) be the largest square root less than or equal to n.Namely:a2(n)=min{m|m≥n12,m∈N+},b2(n)=max{m|m≤n12,m∈N+}.Then define the sequence: S2(n)=[a2(1)+a2(2)+a2(3)+…+a2(n)]/n=1n∑ni=1a2(n),I2(n)=[b2(1)+b2(2)+b2(3)+…+b2(n)]/n=1n∑ni=1b2(n),the smallest square root a2(n)and the largest square root b2(n) of integer n is studied.The elementary and analytic methods to study the mean value properties of these two sequences is used to,give two interesting mean value formulas for them.Based on theorem 1 obtained,then series S2(n)I2(n),K2(n)L2(n),(S2(n)-I2(n)),(K2(n)-L2(n)) are also studied: the convergence and divergence of lemma 1、 lemma 2 and lemma 3." @default.
- W2382036710 created "2016-06-24" @default.
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- W2382036710 date "2010-01-01" @default.
- W2382036710 modified "2023-09-25" @default.
- W2382036710 title "Smarandach Square Parts Sequences a_2(n) and b_2(n)" @default.
- W2382036710 hasPublicationYear "2010" @default.
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