$\frac{1}{\log_a{b}}=\log_b{a}$ 
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．
Options:
  - $$-2$$ 
  - $$-1$$ 
  - $$\frac{1}{2002}$$ 
  - $$\frac{1}{1001}$$ 
  - $$\frac{1}{2}$$ 