Tính nhanh$D = \frac{7}{{1\, \times \,5}}\,\, + \,\,\frac{7}{{5\, \times \,9}}\,\, + \,\frac{7}{{9\, \times \,13}} + \,\frac{7}{{13\, \times \,17}}\, + \,\frac{7}{{17\, \times \,21}}$
Đưa về bài toán tử số bằng hiệu hai thừa số ở mẫu số.
$D = \frac{7}{{1\, \times \,5}}\,\, + \,\,\frac{7}{{5\, \times \,9}}\,\, + \,\frac{7}{{9\, \times \,13}} + \,\frac{7}{{13\, \times \,17}}\, + \,\frac{7}{{17\, \times \,21}}$
$D = 7 \times \left( {\frac{1}{{1 \times 5}} + \frac{1}{{5 \times 9}} + \frac{1}{{9 \times 13}} + \frac{1}{{13 \times 17}} + \frac{1}{{17 \times 21}}} \right)$
$D = \frac{7}{4} \times \left( {\frac{4}{{1 \times 5}} + \frac{4}{{5 \times 9}} + \frac{4}{{9 \times 13}} + \frac{4}{{13 \times 17}} + \frac{4}{{17 \times 21}}} \right)$
$D = \frac{7}{4} \times \left( {1 - \frac{1}{5} + \frac{1}{5} - \frac{1}{9} + \frac{1}{9} - \frac{1}{{13}} + \frac{1}{{13}} - \frac{1}{{17}} + \frac{1}{{17}} - \frac{1}{{21}}} \right)$
$D = \frac{7}{4} \times \left( {1 - \frac{1}{{21}}} \right) = \frac{7}{4} \times \frac{{20}}{{21}} = \frac{5}{3}$
Các bài tập cùng chuyên đề
Tính giá trị$A = \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{{16}} + \frac{1}{{32}} + .... + \frac{1}{{1024}}$
Tính giá trị\(A = \frac{1}{5} + \frac{1}{{10}} + \frac{1}{{20}} + \frac{1}{{40}} + \frac{1}{{80}} + \frac{1}{{160}} + \frac{1}{{320}}\)
Tính giá trị của$C = \frac{3}{2}\,\, + \,\,\frac{3}{8}\,\, + \,\,\frac{3}{{32}}\,\, + \,\,\frac{3}{{128}}\,\, + \,\,\frac{3}{{512}}$
Tính giá trị của $D = \frac{5}{2}\,\, + \frac{5}{6}\,\, + \,\,\frac{5}{{18}}\,\, + \,\,\frac{5}{{54}}\,\, + \,\,\frac{5}{{162}}\,\, + \,\,\frac{5}{{486}}$
Tính nhanh$B = \frac{4}{{3\, \times \,7}}\,\, + \,\,\frac{4}{{7\, \times \,11}}\,\, + \,\,\frac{4}{{11\, \times \,15}}\,\, + \,\frac{4}{{15\, \times \,19}}\,\, + \,\,\frac{4}{{19\, \times \,23}}\,\, + \,\frac{4}{{23\, \times \,27}}$
Tính nhanh$C = \frac{4}{{3\, \times \,6}}\,\, + \,\,\frac{4}{{6\, \times \,9}}\, + \,\frac{4}{{9\, \times \,12}}\, + \,\frac{4}{{12\, \times \,15}}$
Tính nhanh$E = \frac{1}{2} + \frac{1}{6} + \frac{1}{{12}} + \frac{1}{{20}} + \frac{1}{{30}} + \frac{1}{{42}} + .... + \frac{1}{{110}}$
