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P32 [Algebra] - Turkish NMO 1st Round - 2002

Source:

August 11, 2014

Problem Statement

Which of the following is true if S=112+122+132+⋯+120012+120022S = \dfrac 1{1^2} + \dfrac 1{2^2} + \dfrac 1{3^2} + \cdots + \dfrac 1{2001^2} + \dfrac 1{2002^2}?
<spanclass=′latex−bold′>a)</span> 1≤S<43<spanclass=′latex−bold′>b)</span> 43≤S<2<spanclass=′latex−bold′>c)</span> 2≤S<73 <span class='latex-bold'>a)</span>\ 1\leq S < \dfrac 43 \qquad<span class='latex-bold'>b)</span>\ \dfrac 43 \leq S < 2 \qquad<span class='latex-bold'>c)</span>\ 2 \leq S < \dfrac 73 <spanclass=′latex−bold′>d)</span> 73≤S<52<spanclass=′latex−bold′>e)</span> 52≤S<3<span class='latex-bold'>d)</span>\ \dfrac 73 \leq S < \dfrac 52 \qquad<span class='latex-bold'>e)</span>\ \dfrac 52 \leq S < 3
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