Tìm x, biết :
\(\left( {{{11} \over {12}} + {{11} \over {12.23}} + {{11} \over {23.34}} + … + {{11} \over {89.100}}} \right) + x = {5 \over 3}\)
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\(\eqalign{ & \left( {{{11} \over {12}} + {{11} \over {12.23}} + {{11} \over {23.34}} + … + {{11} \over {89.100}}} \right) + x = {5 \over 3} \cr & {{11} \over {12}} + {{23 – 12} \over {12.23}} + {{34 – 23} \over {34.23}} + … + {{100 – 89} \over {89.100}} + x = {5 \over 3} \cr & {{11} \over {12}} + {1 \over {12}} – {1 \over {23}} + {1 \over {23}} – {1 \over {34}} + … + {1 \over {89}} – {1 \over {100}} + x = {5 \over 3} \cr & {{11} \over {12}} + {1 \over {12}} – {1 \over {100}} + x = {5 \over 3} \Leftrightarrow 1 – {1 \over {100}} + x = {5 \over 3} \cr & {{99} \over {100}} + x = {5 \over 3} \Leftrightarrow x = {5 \over 3} – {{99} \over {100}} \Leftrightarrow x = {{500} \over {300}} – {{297} \over {300}} \Leftrightarrow x = {{203} \over {300}}. \cr} \)