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1、 $2002 \frac{1}{2} - 2001 \frac{1}{3} + 2000 \frac{1}{2} - 1999 \frac{1}{3} + \dots + 2 \frac{1}{2} - 1 \frac{1}{3}$

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2、 $(1 - \frac{1}{21} \times 1) + (2 - \frac{1}{21} \times 2) + (3 - \frac{1}{21} \times 3) + (4 - \frac{1}{21} \times 4) + (5 - \frac{1}{21} \times 5) + (6 - \frac{1}{21} \times 6)$

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3、 $\frac{1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \frac{1}{5} - \dots + \frac{1}{19} - \frac{1}{20}}{\frac{1}{1 + 21} + \frac{1}{2 + 22} + \dots + \frac{1}{10 + 30}}$

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4、 $1 + \frac{1}{2} + \frac{2}{2} + \frac{1}{2} + \frac{1}{3} + \frac{2}{3} + \frac{3}{3} + \frac{2}{3} + \frac{1}{3} + \frac{1}{2010} + \frac{2}{2010} + \frac{3}{2010} + \dots + \frac{2}{2010} + \frac{1}{2010}$

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5、 $(\frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{9}) + (\frac{2}{3} + \frac{2}{4} + \dots + \frac{2}{9}) + \dots + (\frac{7}{8} + \frac{7}{9}) + \frac{8}{9}$

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6、 $(1 + \frac{2}{3}) \times (1 + \frac{2}{4}) \times (1 + \frac{2}{5}) \times \dots \times (1 + \frac{2}{22})$

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7、 999.3-998.2+997.3-996.2+…+3.3-2.2+1.3-0.2

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8、 $\frac{\frac{1}{1 \times 2} + \frac{1}{3 \times 4} + \frac{1}{5 \times 6} + \dots + \frac{1}{19 \times 20}}{{\frac{1}{11 \times 20}}^{+} \frac{1}{12 \times 19} + \frac{1}{13 \times 18} + \dots + \frac{1}{15 \times 16}}$

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9、 $24 \times (\frac{1}{2 \times 3} + \frac{1}{4 \times 5} + \dots + \frac{1}{20 \times 21}) -$ $(\frac{1}{1^{2}} + \frac{1}{1^{2} + 2^{2}} + \dots + \frac{1}{1^{2} + 2^{2} + \dots + 10^{2}})$

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10、 $\frac{1^{2} + 2^{2}}{1 \times 2} + \frac{2^{2} + 3^{2}}{2 \times 3} + \frac{3^{2} + 4^{2}}{3 \times 4} + \dots + \frac{202 4^{2} + 202 5^{2}}{2024 \times 2025}$

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11、 $\frac{29}{1 \times 3 \times 5} + \frac{27}{3 \times 5 \times 7} + \frac{25}{5 \times 7 \times 9} + \dots + \frac{1}{29 \times 31 \times 3}$

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12、 $\frac{3}{2} + \frac{7}{6} + \frac{13}{12} + \frac{21}{20} + \dots + \frac{9703}{9702} + \frac{9901}{9900}$

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13、 $\frac{1}{2} + \frac{5}{6} + \frac{11}{12} + \frac{19}{20} + \frac{29}{30} + \frac{41}{42} + \frac{55}{56} + \frac{71}{72} + \frac{89}{90} + \frac{109}{110}$

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14、 $[(\frac{35}{6} - \frac{49}{12} + \frac{63}{20} - \frac{77}{30} + \frac{91}{42} - \frac{105}{56}) - 1 \frac{3}{8}] \div \frac{1}{8}$

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15、 $(\frac{4}{3} - \frac{7}{12} + \frac{11}{28} - \frac{1}{56} - \frac{19}{88} + \frac{30}{209}) \times 19$

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16、 $\frac{7}{2 \times 5}$ - $\frac{13}{5 \times 8}$ + $\frac{19}{8 \times 11}$ - $\frac{25}{11 \times 14}$ + $\frac{31}{14 \times 17}$ - $\frac{37}{17 \times 20}$ + $\frac{43}{20 \times 23}$ - $\frac{49}{23 \times 26}$

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17、 $\frac{\frac{1}{2}}{1 + \frac{1}{2}} + \frac{\frac{1}{3}}{(1 + \frac{1}{2}) \times (1 + \frac{1}{3})} + \frac{\frac{1}{4}}{(1 + \frac{1}{2}) \times (1 + \frac{1}{3}) \times (1 + \frac{1}{4})} + \dots +$ $\frac{\frac{1}{2002}}{(1 + \frac{1}{2}) \times (1 + \frac{1}{3}) \times \dots \times (1 + \frac{1}{2002})}$

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18、 $\frac{1}{3 \times 33} + \frac{3 \times 3 + 1}{33 \times 33} + \frac{3 \times 33 + 1}{33 \times 333} + \frac{3 \times 3333 + 1}{333 \times 33333}$

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19、 $\frac{2^{2}}{1 \times 3} + \frac{4^{2}}{3 \times 5} + \frac{6^{2}}{5 \times 7} + \dots + \frac{100 0^{2}}{99 \times 101}$

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20、 $6 \frac{1}{3} + 12 \frac{1}{6} + 20 \frac{1}{10} + 30 \frac{1}{15} + 42 \frac{1}{21} + 56 \frac{1}{28} + 72 \frac{1}{36}$

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