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C=7/10x11+7/11x12+7/12x13+.................+7/69x70
C=1x7/10x11+1x7/11x12+...........+1x7/69x70
C=7(1/10x11+1/11x12+1/12x13+....+1/69x70)
C=7(1/10-1/11+1/11-1/12+1/12-1/13+.......+1/69-1/70)
C=7(1/10-1/70)
C=7(7/70-1/70)
C=7x6/70
C=3/5
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=1+7+7^2+7^3+...+7^{2016}\)
\(7A=7\left(1+7+7^2+...+7^{2016}\right)\)
\(7A=7+7^2+7^3+...+7^{2017}\)
\(6A=7A-A=7+7^2+7^3+...+7^{2017}-1-7-7^2-...-7^{2016}\)
\(6A=7^{2017}-7\)
\(A=\left(\frac{7^{2017}-7}{6}\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
bạn lên đây xem nha nó có ở bài toán 2 đấy http://d.violet.vn//uploads/resources/609/3303670/preview.swf
A = 7+73+75+77+....+799
72A = 73+75+77+79+.....+7101
48A = 72A - A = 7101 - 7
=> A = \(\frac{7^{101}-7}{48}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:A=7+72+73+...+72010
=>7A=7(7+72+73+...+72010)
7A=49+73+74+...+72011
=>7A-A=(49+73+74+...+72011)-(7+72+73+...+72010)
=>6A=72011-7
=>A=(72011-7):6
Vậy A=(72011-7):6
![](https://rs.olm.vn/images/avt/0.png?1311)
A=7+72 +73+...+7n-1+7n
7A = 72 + 73 + 74 + ... + 7n + 7n+1
7A - A = ( 72 + 73 + 74 + ... + 7n + 7n+1 ) - ( 7+72 +73+...+7n-1+7n )
6A = 7n+1 - 7
A = \(\frac{7^{n+1}-7}{6}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=7^1+7^3+7^5+...+7^{101}\)
\(7A=7^3+7^5+...+7^{102}\)
\(7A-A=7^{102}-7\)
\(6A=7^{102}-7\)
\(A=\frac{7^{102}-7}{6}\)
Vậy ....
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=7^{2022}-7^{2021}+7^{2020}-7^{2019}+...+7^2-7\)
\(\Rightarrow7A=7^{2023}-7^{2022}+7^{2021}-...+7^3-7^2\)
\(\Rightarrow8A=A+7A=7^{2022}-7^{2021}+...+7^2-7+7^{2023}-7^{2022}+...+7^3-7^2=7^{2023}-7\)
\(\Rightarrow A=\dfrac{7^{2023}-7}{8}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Sửa đề: 7/4+7/28+...+7/550
=7/1*4+7/4*7+7/7*10+...+7/22*25
=7/3(1-1/4+1/4-1/7+...+1/22-1/25)
=7/3*24/25=56/25
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