Bài giải:

( Tính nhanh : A= $\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}+\frac{55}{56}+\frac{71}{72}+\frac{89}{90}$ . Viết đáp án dưới dạng a/b )

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

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

= 1 + 1 + 1 + …. + 1 - $\left( \frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90} \right)$

= 9 - $(\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+...+\frac{1}{8\times 9}+\frac{1}{9\times 10})$

= 9 – $(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{8}-\frac{1}{8}+\frac{1}{9}-\frac{1}{10})$

= 9 – ( 1 - $\frac{1}{10}$ )

= 9 - $\frac{9}{10}$ = $\frac{81}{10}$

Vậy đáp số cần điền là : 81/10