2002 AMC 12B Problem 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

\mathrm{(A)}\ -2 \qquad\mathrm{(B)}\ -1 \qquad\mathrm{(C)}\ \frac{1}{2002} \qquad\mathrm{(D)}\ \frac{1}{1001} \qquad\mathrm{(E)}\ \frac 12

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.