c

Hướng dẫn giải

a) \(\frac{1}{{1 \times 2}} + \frac{1}{{2 \times 3}} + \frac{1}{{3 \times 4}} + \ldots + \frac{1}{{8 \times 9}} + \frac{1}{{9 \times 10}}\)

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

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

\( = 1 - \frac{1}{{10}} = \frac{9}{{10}}\)

b) \(\frac{1}{{20}} + \frac{1}{{30}} + \frac{1}{{42}} + \frac{1}{{56}} + \frac{1}{{72}} + \frac{1}{{90}} = \frac{1}{{4 \times 5}} + \frac{1}{{5 \times 6}} + \frac{1}{{6 \times 7}} + \frac{1}{{7 \times 8}} + \frac{1}{{8 \times 9}} + \frac{1}{{9 \times 10}}\)

\( = \frac{1}{4} - \frac{1}{{10}} = \frac{3}{{20}}\)