2*7*7*7
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Lời giải chi tiết:
7 > 6 | 2 < 5 | 7 > 3 | 6 = 6 |
7 > 4 | 5 < 7 | 3 > 1 | 6 < 7 |
7 > 2 | 2 < 7 | 7 > 1 | 7 = 7 |
![](https://rs.olm.vn/images/avt/0.png?1311)
Thực hiện phép nhân và phép chia ở cả 2 vế và so sánh.
Em điền được kết quả như sau:
a) 7 × 5 > 7 × 4 | 7 × 2 = 2 × 7 | 7 × 8 < 7 × 9 |
b) 42 : 7 < 42 : 6 | 21 : 7 = 6 : 2 | 56 : 7 > 49 : 7 |
![](https://rs.olm.vn/images/avt/0.png?1311)
7 x 2 = 14 7 x 4 = 28 7 x 6 = 42 7 x 3 = 21
2 x 7 = 14 4 x 7 = 28 6 x 7 = 42 3 x 7 = 21
14 : 7 = 2 28 : 7 = 4 42 : 7 = 6 21 : 7 = 3
14 : 2 = 7 28 : 4 = 7 42 : 6 = 7 21 : 3 = 7
![](https://rs.olm.vn/images/avt/0.png?1311)
\(1,A=\dfrac{2}{3\cdot7}+\dfrac{2}{7\cdot11}+\dfrac{2}{11\cdot15}+...+\dfrac{2}{99\cdot103}\\ 2A=\dfrac{4}{3\cdot7}+\dfrac{4}{7\cdot11}+\dfrac{4}{11\cdot15}+...+\dfrac{4}{99\cdot103}\\ 2A=\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+...+\dfrac{1}{99}-\dfrac{1}{103}\\ 2A=\dfrac{1}{3}-\dfrac{1}{103}=\dfrac{100}{309}\\ A=\dfrac{100}{309}\cdot\dfrac{1}{2}=\dfrac{50}{309}\)
\(2,A=\dfrac{7}{2}+\dfrac{7}{6}+\dfrac{7}{12}+\dfrac{7}{20}+\dfrac{7}{30}+\dfrac{7}{42}+\dfrac{7}{56}+\dfrac{7}{72}+\dfrac{7}{90}\\ A=7\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{9\cdot10}\right)\\ A=7\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)\\ A=7\left(1-\dfrac{1}{10}\right)=7\cdot\dfrac{9}{10}=\dfrac{63}{10}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=1+7+7^2+7^3+...+7^{2007}\)
\(7A=7+7^2+7^3+7^4+...+7^{2008}\)
\(7A-A=\left(7+7^2+7^3+7^4+...+7^{2008}\right)-\left(1+7+7^2+7^3+...+7^{2007}\right)\)
\(6A=7^{2008}-1\)
\(A=\frac{7^{2008}-1}{6}\)
Tương tự, \(B=\frac{4^{101}-1}{3},C=\frac{3^{101}-1}{2}\).
\(D=7+7^3+7^5+7^7+...+7^{99}\)
\(7^2.D=7^3+7^5+7^7+7^9+...+7^{101}\)
\(\left(7^2-1\right)D=\left(7^3+7^5+7^7+7^9+...+7^{101}\right)-\left(7+7^3+7^5+7^7+...+7^{99}\right)\)
\(48D=7^{101}-7\)
\(D=\frac{7^{101}-7}{48}\)
Tương tự, \(E=\frac{2^{9011}-2}{3}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
2 + 5 = 7 1 + 4 = 5 7 - 6 = 1
7 - 3 = 4 6 + 1 = 7 7 - 4 = 3
4 + 3 = 7 5 + 2 = 7 7 - 0 = 7
![](https://rs.olm.vn/images/avt/0.png?1311)
\(7A=7^2+7^3+...+7^{12}\)
\(\Leftrightarrow A=\dfrac{7^{12}-7}{6}\)
\(7A=7^2+7^3+...+7^{10}+7^{12}\\ 7A-A=7^2+7^3+...+7^{10}+7^{12}-7-7^2-...-7^9-7^{11}\\ 6A=7^{12}-7^{11}+7^{10}-7\\ A=\dfrac{7^{12}-7^{11}+7^{10}-7}{6}\)
686
tick minh nha