huhu, em cũng đang bí câu này

`Answer:`

\(\frac{1}{2}+\frac{2}{8}+\frac{3}{28}+\frac{4}{77}+\frac{5}{176}\)

\(=\frac{1}{1.2}+\frac{2}{2.4}+\frac{3}{4.7}+\frac{4}{7.11}+\frac{5}{11.16}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}\)

\(=1-\frac{1}{16}\)

\(=\frac{15}{16}\)

Giải:

\(\dfrac{1}{2}+\dfrac{2}{8}+\dfrac{3}{28}+\dfrac{4}{77}+\dfrac{5}{176}+\dfrac{6}{352}\) 

\(=\dfrac{1}{1.2}+\dfrac{2}{2.4}+\dfrac{3}{4.7}+\dfrac{4}{7.11}+\dfrac{5}{11.16}+\dfrac{6}{16.22}\) 

\(=\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{22}\) 

\(=\dfrac{1}{1}-\dfrac{1}{22}\) 

\(=\dfrac{21}{22}\)

\(\dfrac{1}{2}+\dfrac{2}{8}+\dfrac{3}{28}+\dfrac{4}{77}+\dfrac{5}{176}+\dfrac{6}{352}\\ =\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{3}{28}+\dfrac{4}{77}+\dfrac{5}{176}+\dfrac{3}{176}\\ =\dfrac{3}{4}+\dfrac{3}{28}+\dfrac{4}{77}+\dfrac{1}{22}\\ =\dfrac{21}{28}+\dfrac{3}{28}+\dfrac{7}{154}+\dfrac{8}{154}\\ =\dfrac{6}{7}+\dfrac{15}{154}\\ =\dfrac{21}{22}\)

\(\dfrac{1}{2}+\dfrac{2}{8}+\dfrac{3}{28}+\dfrac{4}{77}+\dfrac{5}{176}+\dfrac{6}{352}=\dfrac{1}{1.2}+\dfrac{2}{2.4}+\dfrac{3}{4.7}+\dfrac{4}{7.11}+\dfrac{5}{11.16}+\dfrac{6}{16.22}=1-\dfrac{1}{22}=\dfrac{21}{22}\)

1/2 x 2/8 x 3/28 x 4/77 x 5/176

\(=\frac{1.2.3.4.5}{2.8.28.77.176}=\frac{1.2.3.4.5}{2.2.4.7.4.11.4.4}=\frac{3.5}{2.7.4.4.11.4}=\frac{15}{9856}\)

bạn học lớp 6b phải ko

=   15

     16          

\(\frac{15}{16}\)

\(\frac{15}{16}\)

Giải:

\(\dfrac{3}{2}+\dfrac{6}{8}+\dfrac{9}{28}+\dfrac{12}{77}+\dfrac{15}{176}\) 

\(=\dfrac{3}{1.2}+\dfrac{6}{2.4}+\dfrac{9}{4.7}+\dfrac{12}{7.11}+\dfrac{15}{11.16}\) 

\(=3.\left(\dfrac{1}{1.2}+\dfrac{2}{2.4}+\dfrac{3}{4.7}+\dfrac{4}{7.11}+\dfrac{5}{11.16}\right)\) 

\(=3.\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}\right)\) 

\(=3.\left(1-\dfrac{1}{16}\right)\) 

\(=3.\dfrac{15}{16}\) 

\(=\dfrac{45}{16}\)

Đặt A = \(\dfrac{3}{2}+\dfrac{6}{8}+\dfrac{9}{28}+\dfrac{12}{77}+\dfrac{15}{176}\)

= \(3\left(\dfrac{1}{1\times2}+\dfrac{2}{2\times4}+\dfrac{3}{4\times7}+\dfrac{4}{7\times11}+\dfrac{5}{11\times16}\right)\)

= \(3\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}\right)\)

= \(3\left(1-\dfrac{1}{16}\right)=3\times\dfrac{15}{16}=\dfrac{45}{16}\)