$S = \dfrac 1{1^2} + \dfrac 1{2^2} + \dfrac 1{3^2} + \cdots + \dfrac 1{2001^2} + \dfrac 1{2002^2}$ ise, aşağıdakilerden hangisi doğrudur?
$
\textbf{a)}\ 1\leq S < \dfrac 43
\qquad\textbf{b)}\ \dfrac 43 \leq S < 2
\qquad\textbf{c)}\ 2 \leq S < \dfrac 73
\qquad\textbf{d)}\ \dfrac 73 \leq S < \dfrac 52
\qquad\textbf{e)}\ \dfrac 52 \leq S < 3
$