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