Tính giá trị biểu thức dưới đây C = 1/2 + 5/6 + 11/12 + 19/20 + 29/30 + 41/42 + 55/56 + 71/72 + 89/90

\[C = \frac{1}{2} + \frac{5}{6} + \frac{{11}}{{12}} + \frac{{19}}{{20}} + \frac{{29}}{{30}} + \frac{{41}}{{42}} + \frac{{55}}{{56}} + \frac{{71}}{{72}} + \frac{{89}}{{90}}\]

\[ = 1 - \frac{1}{2} + 1 - \frac{1}{6} + 1 - \frac{1}{{12}} + 1 - \frac{1}{{20}} + 1 - \frac{1}{{30}} + 1 - \frac{1}{{42}} + 1 - \frac{1}{{56}} + 1 - \frac{1}{{72}} + 1 - \frac{1}{{90}}\]

\[ = 9 - \left( {\frac{1}{2} + \frac{1}{6} + \frac{1}{{12}} + \frac{1}{{20}} + \frac{1}{{30}} + \frac{1}{{42}} + \frac{1}{{56}} + \frac{1}{{72}} + \frac{1}{{90}}} \right)\]

\[ = 9 - \left( {\frac{1}{{1 \cdot 2}} + \frac{1}{{2 \cdot 3}} + \frac{1}{{3 \cdot 4}} + \frac{1}{{4 \cdot 5}} + \frac{1}{{5 \cdot 6}} + \frac{1}{{6 \cdot 7}} + \frac{1}{{7 \cdot 8}} + \frac{1}{{8 \cdot 9}} + \frac{1}{{9 \cdot 10}}} \right)\]

\[ = 9 - \left( {1 - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + \frac{1}{3} - \frac{1}{4} + ... + \frac{1}{9} - \frac{1}{{10}}} \right)\]

\[ = 9 - \left( {1 - \frac{1}{{10}}} \right)\]

\[ = 9 - \frac{9}{{10}} = \frac{{81}}{{10}}.\]

Vậy \[C = 9 - \frac{9}{{10}} = \frac{{81}}{{10}}.\]