(CHINA TST 2009) CHO SỐ NGUYÊN N2. TÌM HẰNG SỐ  N LỚN NHẤT...

Bài 7 (China TST 2009) Cho số nguyên

n

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2.

Tìm hằng số ^

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lớn nhất có tính chất sau: Nếu dãy các số thực lõm

a a

₀

, ,...,

₁

a

_n

thỏa mãn

0



a

₀

 

a

₁

a

₂

 

...

a

_n

thì

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n

n

2

 

2

ia



n

a





i

i







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1

1

TÀI LIỆU THAM KHẢO

[1]. Chikkanna R. Selvaraj, Suguna Selvaraj,

Summability Matrices and Mean – Convex Sequense,

Int. J. Contemp. Math. Sciences, Vol.8, 2013, No. 19

[2]. Feng Qi, Bainiguo,

Monotonicity of Sequences Involving Convex Function and Sequence, 2000

Mathematics Subject Classification.

[3]. Katarina Nicova, A Note On Higher – Order Convexity of Sequences, Int. J. of Pure and Applied

Mathematics, Volume 83 No. 1, 2013

[4]. Lily L.Liu, Yi Wang, On the log – Convexity of Combinatorial Sequenses, Partially Supported by

NSF of China 10471016

[5]. A. McD. Mercer, Polynomials and Convex Sequence Inequalities, Journal of Inequalities In Pure

and Applied Mathematics, Volume 6, Issue 1, Article 8, 2005

[6]. Moussa Ahmia, Hacine Belbachir,

Preserving log – convexity for Generalized Pascal triangles,

The Electronic Journal of Combinatorics 19(2) (2012)

[7]. Shanhe Wu, Lokenath Debnath, A Computers and Mathematics with Applications 54 (2007)

[8]. Zinelabidine LaTreuch, Benharrat Belaidi, New Inequalities for Convex Sequences

[9]. IMO Shortlist (1959 – 2016)

[10]. Diễn đàn AoPS.