Tính \(A=\frac{7^2}{2.9}+\frac{7^2}{9.16}+\frac{7^2}{16.23}+..........+\frac{7^2}{65.72}\)
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DP
2 tháng 8 2017
\(C=\frac{7^2}{2.9}+\frac{7^2}{9.16}+\frac{7^2}{16.23}+...+\frac{7^2}{65.72}\)
\(C=\frac{7^2}{7}.\left(\frac{1}{2}-\frac{1}{9}+\frac{1}{9}-\frac{1}{16}+\frac{1}{16}-\frac{1}{23}+...+\frac{1}{65}-\frac{1}{72}\right)\)
\(C=7.\left(\frac{1}{2}-\frac{1}{72}\right)\)
\(C=7.\frac{35}{72}=\frac{245}{72}\)
2 tháng 8 2017
Ta có : \(C=\frac{7^2}{2.9}+\frac{7^2}{9.16}+\frac{7^2}{16.23}+.....+\frac{7^2}{65.72}\)
\(\Rightarrow C=7\left(\frac{7}{2.9}+\frac{7}{9.16}+\frac{7}{16.23}+.....+\frac{7}{65.72}\right)\)
\(\Rightarrow C=7\left(\frac{1}{2}-\frac{1}{9}+\frac{1}{9}-\frac{1}{16}+.....+\frac{1}{65}-\frac{1}{72}\right)\)
\(\Rightarrow C=7\left(\frac{1}{2}-\frac{1}{72}\right)\)
\(\Rightarrow C=7.\frac{35}{72}=\frac{245}{72}\)
DP
18 tháng 7 2017
\(C=\frac{7^2}{2.9}+\frac{7^2}{9.16}+\frac{7^2}{16.23}+....+\frac{7^2}{65.72}\)
\(C=\frac{7^2}{7}\cdot\left(\frac{1}{2}-\frac{1}{9}+\frac{1}{9}-\frac{1}{16}+\frac{1}{16}-\frac{1}{23}+....+\frac{1}{65}-\frac{1}{72}\right)\)
\(C=7\cdot\left(\frac{1}{2}-\frac{1}{72}\right)\)
\(C=7\cdot\frac{35}{72}=\frac{245}{72}\)
17 tháng 7 2017
C = 49(1/2.9 ... 1/65.72)
C = 49(1/2 - 1/9 +....+ 1/65 - 1/72)
C = 49( 1/2 - 1/72)
C = bạn tự tính nhé
Có j không hiểu thì Ib mình
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 = \(7.\frac{35}{72}=\frac{245}{72}\)
CC
20 tháng 7 2019
Nhìn kĩ là ra thôi :
\(\frac{7^2}{2.9}+\frac{7^2}{9.16}+...+\frac{7^2}{65.72}\)
= \(7\left(\frac{7}{2.9}+\frac{7}{9.16}+...+\frac{7}{65.72}\right)\)
= \(7\left(\frac{1}{2}-\frac{1}{9}+\frac{1}{9}-\frac{1}{16}+...+\frac{1}{65}-\frac{1}{72}\right)\)
= \(7\left(\frac{1}{2}-\frac{1}{72}\right)\)
= \(7.\frac{35}{72}=3\frac{29}{72}\)
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 !!!
TN
2
PT
9 tháng 12 2017
\(\dfrac{7^2}{2.9}+\dfrac{7^2}{9.16}+\dfrac{7^2}{16.23}+...+\dfrac{7^2}{65.72}\)
\(=7^2\left(\dfrac{1}{2.9}+\dfrac{1}{9.16}+\dfrac{1}{16.23}+...+\dfrac{1}{65.72}\right)\)
\(=7^2\left(\dfrac{1}{2}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{23}+...+\dfrac{1}{65}-\dfrac{1}{72}\right)\)
\(=7^2\left(\dfrac{1}{2}-\dfrac{1}{72}\right)\)
\(=49\left(\dfrac{35}{72}\right)\)
\(=\dfrac{1715}{72}\)
9 tháng 12 2017
\(l=\dfrac{7^2}{2.9}+\dfrac{7^2}{9.16}+\dfrac{7^2}{16.23}+...+\dfrac{7^2}{65.72}\)
\(=7\left(\dfrac{7}{2.9}+\dfrac{7}{9.16}+\dfrac{7}{16.23}+...+\dfrac{7}{65.72}\right)\)
\(=7\left(\dfrac{1}{2}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{23}+...+\dfrac{1}{65}-\dfrac{1}{72}\right)\)
\(=7\left(\dfrac{1}{2}-\dfrac{1}{72}\right)=7\left(\dfrac{36}{72}-\dfrac{1}{72}\right)=7.\dfrac{35}{72}=\dfrac{245}{72}\)
O
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
\(\dfrac{B}{7}=\dfrac{7}{2\cdot9}+\dfrac{7}{9\cdot16}+\dfrac{7}{16\cdot23}+...+\dfrac{49}{65\cdot72}\\ \dfrac{B}{7}=\dfrac{1}{2}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{23}+...+\dfrac{1}{65}-\dfrac{1}{72}\\ \dfrac{B}{7}=\dfrac{1}{2}-\dfrac{1}{72}\\ \dfrac{B}{7}=\dfrac{35}{72}\\ B=\dfrac{35}{72}\times7\\ B=\dfrac{245}{72} \)
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
\(A=\frac{7^2}{2.9}+\frac{7^2}{9.16}+\frac{7}{16.23}+.....+\frac{7^2}{65.72}\)
=\(7.\left(\frac{1}{2}-\frac{1}{9}+\frac{1}{9}-\frac{1}{16}+\frac{1}{16}-\frac{1}{23}+....+\frac{1}{65}-\frac{1}{72}\right)\)
=\(7.\left(\frac{1}{2}-\frac{1}{72}\right)\)
=\(7.\frac{35}{72}\)
=\(\frac{245}{72}\)