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’98高考数学压轴题,即第25题(理):已知数列{b_n}是等差数列,b_1=1,b_1+b_2+……+b_(10)=145.(Ⅰ)求数列{b_n}的通项b_n;(Ⅱ)设数列{a_n}的通项a_n=log_a(1+1/b_n)(其中a>0且a≠1),记S_n是数列{a_n}的前n项和。试比较S_n与1/3log_ab_(n+1)的大小,并证明你的结论。此题旨在考查等差数列基本概念及其通项求法,考查对数函数性质,考查归纳、推理能力以及用数学归纳法进行论证的能力。解法一:利用数学归纳法求证
’98 college entrance examination mathematics scroll title, that is, the 25th question (Science): Known series {b_n} is an arithmetic sequence, b_1=1,b_1+b_2+...+b_(10)=145.(I)Seek series {b_n General term b_n of }; (II) Set the general term a_n=log_a(1+1/b_n) of the series {a_n} (where a>0 and a≠1), and note that S_n is the first n terms of the series {a_n} . Compare the size of S_n with 1/3log_ab_(n+1) and prove your conclusion. This question is intended to examine the basic concepts of arithmetic progression and its general term method, to examine the nature of logarithmic functions, to examine the ability of inductive and inferential, and to use mathematical induction for argumentation. Solution One: Using Mathematical Induction to Prove