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题目(2013年广东省高考理科数学第19题)设数列{an}的前n项和为Sn,已知a1=1,2S_n/n=a_(n+1)-1/3n~2-n-2/3,n∈N~*.(1)求a2的值;(2)求数列{an}的通项公式;(3)证明:对一切正整数n,有1/a_1+1/a_2+…+1/a_n<7/4.本题考查了递推公式、等差数列的概念、通项公式、裂项相消法求数列的前n项和、放缩法证明不等式等知识.要求a2,需要建立关于a2的方程,考查了方程思想.要求数列的通
(2013 Guangdong Provincial College entrance examination science math problem 19) set the number of columns {an} the first n and is Sn, known a1 = 1,2S_n / n = a_ (n +1) -1 / 3n ~ 2-n -2 / 3, n∈N ~ *. (1) Find the value of a2; (2) Find the general formula of {an}; (3) Prove that for every positive integer n, 1 / a_1 + a_2 + ... + 1 / a_n <7/4. This paper examines the recursion formula, the concept of arithmetic progression, the general formula, the first n terms of the sequence of fission terms and the inequality of scaling law. a2, need to establish the equation on a2, examining the idea of the equation