\({1 \over 3} - {1 \over {12}} - {1 \over {20}} - {1 \over {30}} - {1 \over {42}} - {1 \over {56}} - {1 \over {72}} - {1 \over {90}} - {1 \over {110}} = x - {5 \over {13}}\)
\(\eqalign{& {1 \over 3} - \left( {{1 \over {12}} + {1 \over {20}} + {1 \over {30}} + {1 \over {42}} + {1 \over {56}} + {1 \over {72}} + {1 \over {90}} + {1 \over {110}}} \right) = x - {5 \over {13}} \cr & {1 \over 3} - \left( {{1 \over {3.4}} + {1 \over {4.5}} + {1 \over {5.6}} + {1 \over {6.7}} + {1 \over {7.8}} + {1 \over {8.9}} + {1 \over {9.10}} + {1 \over {10.11}}} \right) = x - {5 \over {13}} \cr & {1 \over 3} - \left( {{1 \over 3} - {1 \over 4} + {1 \over 4} - {1 \over 5} + {1 \over 5} - {1 \over 6} + ... + {1 \over 9} - {1 \over {10}} + {1 \over {10}} - {1 \over {11}}} \right) = x - {5 \over {13}} \cr & {1 \over 3} - \left( {{1 \over 3} - {1 \over {11}}} \right) = x - {5 \over {13}} \cr & {1 \over 3} - {1 \over 3} + {1 \over {11}} = x - {5 \over {13}} \cr} \)
\(\eqalign{& {1 \over {11}} = x - {5 \over {13}} \cr & x = {1 \over {11}} + {5 \over {13}} \cr & x = {{13} \over {143}} + {{55} \over {143}} \cr & x = {{68} \over {143}}. \cr} \)
