2002年AMC12竞赛B第22题
2002AMC12B, 22  For all integers $$n$$ greater than $$1$$, define $$a_{n}=\frac{1}{\log _{n}2002}$$.  Let $$b=a_{2}+a_{3}+a_{4}+a_{5}$$ and $$c=a_{10}+a_{11}+a_{12}+a_{13}+a_{14}$$. Then $$b-c$$ equals．  对于大于$$1$$的所有整数$$n$$，定义$$a_{n}=\frac{1}{\log _{n}2002}$$。令 $$b=a_{2}+a_{3}+a_{4}+a_{5}$$，$$c=a_{10}+a_{11}+a_{12}+a_{13} +a_{14}$$。则 $$b-c$$ 等于．
课内体系->知识点->基本初等函数->对数的概念及其运算->对数的运算 美国AMC10/12->Knowledge Point->Algebra->Sequence->Sum of the First n Terms for Geometric Sequences
$\frac{1}{\log_a{b}}=\log_b{a}$ 