分数計算テクニック
{1} over {2} + {1} over {6} + {1} over {12} + {1} over {20} + {1} over {30} + {1} over {42} + {1} over {56} + {1} over {72} + {1} over {90}
= {1} over { 1 times 2 } + {1} over { 2 times 3 } + {1} over { 3 times 4 } + {1} over { 4 times 5 } + {1} over { 5 times 6 } + {1} over { 6 times 7 } + {1} over { 7 times 8 } + {1} over { 8 times 9 } + {1} over { 9 times 10 }
left ( {1} over {1} - {1} over {2} right ) + left ( {1} over {2} - {1} over {3} right ) + left ( {1} over {3} - {1} over {4} right ) + left ( {1} over {4} - {1} over {5} right ) + left ( {1} over {5} - {1} over {6} right ) + left ( {1} over {6} - {1} over {7} right ) + left ( {1} over {7} - {1} over {8} right ) + left ( {1} over {8} - {1} over {9} right ) + left ( {1} over {9} - {1} over {10} right )
{1} over {1} - {1} over {2} + {1} over {2} - {1} over {3} + {1} over {3} - {1} over {4} + {1} over {4} - {1} over {5} + {1} over {5} - {1} over {6} + {1} over {6} - {1} over {7} + {1} over {7} - {1} over {8} + {1} over {8} - {1} over {9} + {1} over {9} - {1} over {10}
{1} over {1} - {1} over {10}
---{1} over {1} - {1} over {10}
{1} over {3}+ {1} over {15}+ {1} over {35}+ {1} over {63} + {1} over {99} + {1} over {143} + {1} over {195} + {1} over {255} + {1} over {323}
{1} over { 1 times 3 } + {1} over { 3 times 5 } + {1} over { 5 times 7 } + {1} over { 7 times 9 } + {1} over { 9 times 11 } + {1} over { 11 times 13 } + {1} over { 13 times 15 } + {1} over { 15 times 17 } + {1} over { 17 times 19 }
{1} over {2} left ( {2} over { 1 times 3 } + {2} over { 3 times 5 } + {2} over { 5 times 7 } + {2} over { 7 times 9 } + {2} over { 9 times 11 } + {2} over { 11 times 13 } + {2} over { 13 times 15 } + {2} over { 15 times 17 } + {2} over { 17 times 19 } right ){1} over {2} left ( {3 - 1} over { 1 times 3 } + {5-3} over { 3 times 5 } + {7-5} over { 5 times 7 } + {9-7} over { 7 times 9 } + {11-9} over { 9 times 11 } + {13-11} over { 11 times 13 } + {15 - 13} over { 13 times 15 } + {17 - 15} over { 15 times 17 } + {19 - 17} over { 17 times 19 } right )
{1} over {2} left ( left ( {1} over {1} - {1} over {3} right ) + left ( {1} over {3} - {1} over {5} right ) + left ( {1} over {5} - {1} over {7} right ) + left ( {1} over {7} - {1} over {9} right ) + left ( {1} over {9} - {1} over {11} right ) + left ( {1} over {11} - {1} over {13} right ) + left ( {1} over {13} - {1} over {15} right ) + left ( {1} over {15} - {1} over {17} right ) + left ( {1} over {17} - {1} over {19} right ) right )
{1} over {2} left ( {1} over {1} - {1} over {3} + {1} over {3} - {1} over {5} + {1} over {5} - {1} over {7} + {1} over {7} - {1} over {9} + {1} over {9} - {1} over {11} + {1} over {11} - {1} over {13} + {1} over {13} - {1} over {15} + {1} over {15} - {1} over {17} + {1} over {17} - {1} over {19} right )
{1} over {2} left ( {1} over {1} - {1} over {19} right )
{ {1} over {2} } times { {18} over {19} }
---
{1} over {4}+ {1} over {28}+ {1} over {70}+ {1} over {130} + {1} over {208} + {1} over {304}
{1} over { 1 times 4 } + {1} over { 4 times 7 } + {1} over { 7 times 10 } + {1} over { 10 times 13 } + {1} over { 13 times 16 } + {1} over { 16 times 19 }
{1} over {3} left ( {3} over { 1 times 4 } + {3} over { 4 times 7 } + {3} over { 7 times 10 } + {3} over { 10 times 13 } + {3} over { 13 times 16 } + {3} over { 16 times 19 } right ){1} over {3} left ( {4 - 1} over { 1 times 4 } + {7 - 4} over { 4 times 7 } + {10 - 7} over { 7 times 10 } + {13 - 10} over { 10 times 13 } + {16 - 13} over { 13 times 16 } + {19 - 16} over { 16 times 19 } right )
{1} over {3} left ( left ( {1} over {1} - {1} over {4} right ) + left ( {1} over {4} - {1} over {7} right ) + left ( {1} over {7} - {1} over {10} right ) + left ( {1} over {10} - {1} over {13} right ) + left ( {1} over {13} - {1} over {16} right ) + left ( {1} over {16} - {1} over {19} right ) right )
{1} over {3} left ( {1} over {1} - {1} over {4} + {1} over {4} - {1} over {7} + {1} over {7} - {1} over {10} + {1} over {10} - {1} over {13} + {1} over {13} - {1} over {16} + {1} over {16} - {1} over {19} right )
{1} over {3} left ( {1} over {1} - {1} over {19} right )
{ {1} over {3} } times { {18} over {19} }
