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13 tháng 3 2022

\(B=\dfrac{1}{7}\left(\dfrac{1}{2}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{16}+...+\dfrac{1}{107}-\dfrac{1}{114}\right)\)

\(=\dfrac{1}{7}\left(\dfrac{1}{2}-\dfrac{1}{114}\right)=\dfrac{4}{57}\)

3 tháng 8 2015

1/3.10+1/10.17+......+1/73.80 - 1/2.9 - 1/9.16  -  1/16.23  -  1/23.30

= (7/3.10+7/10.17+......+7/73.80) : 7 - (7/2.9 + 7/9.16  +  7/16.23  +  7/23.30) : 7

= (1/3-1/10+1/10-1/17+...+1/73-1/80) : 7 - (1/2-1/9+1/9-1/16+1/16-1/23+1/23-1/30) : 7

=(1/3-1/80) : 7 - (1/2-1/30) : 7

= 77/240 : 7 - 7/15 : 7

=11/240 - 1/15

= -1/48

Nhấn đúng cho mk nha!!!!!!!!!!!!!

 

11 tháng 5 2022

\(B=\dfrac{49}{2\cdot9}+\dfrac{49}{9\cdot16}+\dfrac{49}{16\cdot23}+...+\dfrac{49}{65\cdot72}\)

\(B=\dfrac{49}{7}\cdot\left(\dfrac{1}{2}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{23}+...+\dfrac{1}{65}-\dfrac{1}{72}\right)\)

\(B=7\cdot\left(\dfrac{1}{2}-\dfrac{1}{72}\right)\)

\(B=7\cdot\left(\dfrac{36}{72}-\dfrac{1}{72}\right)\)

\(B=7\cdot\dfrac{35}{72}\)

\(B=\dfrac{\left(7\cdot35\right)}{72}\)

\(B=\dfrac{245}{72}\)

11 tháng 5 2022

\(\dfrac{B}{7}=\dfrac{7}{2\cdot9}+\dfrac{7}{9\cdot16}+\dfrac{7}{16\cdot23}+...+\dfrac{49}{65\cdot72}\\ \dfrac{B}{7}=\dfrac{1}{2}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{23}+...+\dfrac{1}{65}-\dfrac{1}{72}\\ \dfrac{B}{7}=\dfrac{1}{2}-\dfrac{1}{72}\\ \dfrac{B}{7}=\dfrac{35}{72}\\ B=\dfrac{35}{72}\times7\\ B=\dfrac{245}{72} \)

22 tháng 3 2016

A = 7 (7 / 2.9 + 7 / 9.16 + .......... + 7/65.72)

A=7( 1/2 - 1/9 +1/9 - 1/16 +......+1/65 - 1/72)

A= 7 ( 1/2 -1/72)

A= 7 . 35/72

A=245/72

22 tháng 3 2016

\(A=\frac{7^2}{2.9}+\frac{7^2}{9.16}+\frac{7}{16.23}+.....+\frac{7^2}{65.72}\)

=\(7.\left(\frac{1}{2}-\frac{1}{9}+\frac{1}{9}-\frac{1}{16}+\frac{1}{16}-\frac{1}{23}+....+\frac{1}{65}-\frac{1}{72}\right)\)

=\(7.\left(\frac{1}{2}-\frac{1}{72}\right)\)

=\(7.\frac{35}{72}\)

=\(\frac{245}{72}\)

3 tháng 9 2017

\(F=\dfrac{49}{2.9}+\dfrac{49}{9.16}+............+\dfrac{49}{65.72}\)

\(\Leftrightarrow F=\dfrac{7^2}{2.9}+\dfrac{7^2}{9.16}+............+\dfrac{7^2}{65.72}\)

\(\Leftrightarrow F=7\left(\dfrac{7}{2.9}+\dfrac{7}{9.16}+.............+\dfrac{7}{65.72}\right)\)

\(\Leftrightarrow F=7\left(\dfrac{1}{2}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{16}+...........+\dfrac{1}{65}-\dfrac{1}{75}\right)\)

\(\Leftrightarrow F=7\left(\dfrac{1}{2}-\dfrac{1}{72}\right)\)

\(\Leftrightarrow F=7.\dfrac{35}{72}=\dfrac{245}{72}\)

\(G=\dfrac{3}{1.3}+\dfrac{3}{3.5}+...........+\dfrac{3}{47.49}\)

\(\Leftrightarrow G=\dfrac{3.2}{1.3.2}+\dfrac{3.2}{3.5.2}+........+\dfrac{3.2}{47.49}\)

\(\Leftrightarrow G=\dfrac{3}{2}\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+..........+\dfrac{2}{47.49}\right)\)

\(\Leftrightarrow G=\dfrac{3}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+........+\dfrac{1}{47}-\dfrac{1}{49}\right)\)

\(\Leftrightarrow G=\dfrac{3}{2}\left(1-\dfrac{1}{49}\right)\)

\(\Leftrightarrow G=\dfrac{3}{2}.\dfrac{48}{49}=\dfrac{72}{49}\)

8 tháng 5 2017

Đặt \(A=\frac{7^2}{2.9}+\frac{7^2}{9.16}+\frac{7^2}{16.23}+\frac{7^2}{23.30}\)

\(\Rightarrow A=7.\left(\frac{1}{2}-\frac{1}{9}+\frac{1}{9}-\frac{1}{16}+\frac{1}{16}-\frac{1}{23}+\frac{1}{23}-\frac{1}{30}\right)\)

\(\Rightarrow A=7.\left(\frac{1}{2}-\frac{1}{30}\right)\)

\(\Rightarrow A=\frac{49}{15}\)

8 tháng 5 2017

đặt biểu thức là B

Ta có công thức :

\(\frac{a}{b.c}=\frac{a}{c-b}.\left(\frac{1}{b}-\frac{1}{c}\right)\)

Dựa vào công thức, ta có :

\(B=7.\left(\frac{1}{2}-\frac{1}{9}+\frac{1}{9}-\frac{1}{16}+.....+\frac{1}{23}-\frac{1}{30}\right)\)

\(B=7.\left(\frac{1}{2}-\frac{1}{30}\right)=7.\frac{7}{15}=\frac{49}{15}\)

Ai thấy đúng thì ủng hộ nha !!!

20 tháng 7 2019

Ta có: 

C = \(\frac{7^2}{2.9}+\frac{7^2}{9.16}+\frac{7^2}{16.23}+...+\frac{7^2}{65.72}\)

=> C = \(7.\left(\frac{7}{2.9}+\frac{7}{9.16}+\frac{7}{16.23}+...+\frac{7}{65.72}\right)\)

=> C = \(7.\left(\frac{1}{2}-\frac{1}{9}+\frac{1}{9}-\frac{1}{16}+\frac{1}{16}-\frac{1}{23}+...+\frac{1}{65}-\frac{1}{72}\right)\)

=> C = \(7.\left(\frac{1}{2}-\frac{1}{72}\right)\)

=> C = \(7.\frac{35}{72}=\frac{245}{72}\)

20 tháng 7 2019

Nhìn kĩ là ra thôi :

 \(\frac{7^2}{2.9}+\frac{7^2}{9.16}+...+\frac{7^2}{65.72}\)

\(7\left(\frac{7}{2.9}+\frac{7}{9.16}+...+\frac{7}{65.72}\right)\)

\(7\left(\frac{1}{2}-\frac{1}{9}+\frac{1}{9}-\frac{1}{16}+...+\frac{1}{65}-\frac{1}{72}\right)\)

\(7\left(\frac{1}{2}-\frac{1}{72}\right)\)

\(7.\frac{35}{72}=3\frac{29}{72}\)