Tính :
\(S = \left( {1 – {1 \over {{2^2}}}} \right).\left( {1 – {1 \over {{3^2}}}} \right)…\left( {1 – {1 \over {{{10}^2}}}} \right)\)
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\(\eqalign{ & S = \left( {1 – {1 \over {{2^2}}}} \right).\left( {1 – {1 \over {{3^2}}}} \right)…\left( {1 – {1 \over {{{10}^2}}}} \right) = \left( {{{{2^2}} \over {{2^2}}} – {1 \over {{2^2}}}} \right).\left( {{{{3^2}} \over {{3^2}}} – {1 \over {{3^2}}}} \right)…\left( {{{{{10}^2}} \over {{{10}^2}}} – {1 \over {{{10}^2}}}} \right) \cr & = {3 \over {{2^2}}}.{8 \over {{3^2}}}.{{15} \over {{4^2}}}…{{80} \over {{9^2}}}.{{99} \over {{{10}^2}}} = {{(1.3).(2.4).(3.5)…(8.10).(9.11)} \over {{2^2}{{.3}^2}{{.4}^2}{{…9}^2}{{.10}^2}}} = {{(1.2.3…9)(4.5…1)} \over {(2.3.4…9.10).(2.3…9.10)}} = {{1.11} \over {10.2}} = {{11} \over {20}} \cr} \)