tính tổng 1/1.6 +1/6.11 +......+1/496.501
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![](https://rs.olm.vn/images/avt/0.png?1311)
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5S=5.(1/1.6+1/6.11+...+1/496.501)
5S=5/1.6+5/6.11+...+5/496.501
5S=1/1-1/6+1/6-1/11+...+1/496-1/501
5S=1-1/501
5S=500/501
S=500/501:5=100/501
k nhé
ta co:5S=5/1.6+5/6.11+5/11.16+...+5/496.501
=1-1/6+1/6-1/11+1/11-1/16+.....+1/496-1/501
=1-1/501=500/501
=>S=500/501:5=100/501
MK đau tien nha bn
![](https://rs.olm.vn/images/avt/0.png?1311)
1/1.6 + 1/6.11+ 1/11.16+ ....
số thứ 100 có dạng 1/(496.501)
do đó tổng trên bằng :
1/5( 1/1- 1/501)
= 100/ 501
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+....+\frac{1}{496}-\frac{1}{501}\right):5\)
\(A=\left(1-\frac{1}{501}\right):5\)
\(A=\frac{500}{501}:5=\frac{100}{501}\)
Ta có : \(A=\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{496.501}\)
\(\Rightarrow\) \(A=\frac{1}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{496}-\frac{1}{501}\right) \)
\(\Rightarrow\) \(A=\frac{1}{5}\left(1-\frac{1}{501}\right)\)
\(\Rightarrow\) \(A=\frac{1}{5}.\frac{501-1}{501}=\frac{1}{5}.\frac{500}{501}\)
\(\Rightarrow\) \(A=\frac{1.500}{5.501}=\frac{20}{1.501}=\frac{20}{501}\)
Vậy \(A=\frac{20}{501}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Lời giải:
\(5A=\frac{6-1}{1.6}+\frac{11-6}{6.11}+\frac{16-11}{11.16}+....+\frac{501-496}{496.501}\)
\(=\frac{6}{1.6}-\frac{1}{1.6}+\frac{11}{6.11}-\frac{6}{6.11}+\frac{16}{11.16}-\frac{11}{11.16}+...+\frac{501}{496.501}-\frac{496}{496.501}\)
\(=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+....+\frac{1}{496}-\frac{1}{501}=1-\frac{1}{501}=\frac{500}{501}\)
$\Rightarrow A=\frac{100}{501}$
\(A=\dfrac{1}{5}\left(\dfrac{1}{1.6}+...+\dfrac{1}{496.501}\right)\)
\(A=\dfrac{1}{5}\left(1-\dfrac{1}{6}+\cdot\cdot\cdot+\dfrac{1}{495}-\dfrac{1}{501}\right)\)
\(A=\dfrac{1}{5}\left(1-\dfrac{1}{501}\right)\)
\(A=\dfrac{1}{5}\cdot\dfrac{500}{501}=\dfrac{100}{501}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Giải
= 1/5 . ( 1 - 1/6 + 1/6 - 1/11 + . ... + 1/496 - 1/501)
= 1/5 . ( 1-1/501)
= 1/5 . 500/501
= 100/501
Bạn nhân trên tử vào 6 tất cả các phân số! Rồi tách ra là làm đc thui!
![](https://rs.olm.vn/images/avt/0.png?1311)
a, Đặt \(A=\dfrac{3}{1.6}+\dfrac{3}{6.11}+...+\dfrac{3}{496.501}\)
\(5A=\dfrac{3.5}{1.6}+\dfrac{3.5}{6.11}+...+\dfrac{3.5}{496.501}\)
\(5A=3\left(\dfrac{5}{1.6}+\dfrac{5}{6.11}+...+\dfrac{5}{496.501}\right)\)
\(5A=3\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{496}-\dfrac{1}{501}\right)\)
\(5A=3\left(1-\dfrac{1}{501}\right)\)
\(5A=3\cdot\dfrac{500}{501}\)
\(A=\dfrac{1500}{501}:5\)
\(A=\dfrac{100}{167}\)
b, Đặt \(B=\dfrac{1}{2^3}+\dfrac{1}{2^4}+...+\dfrac{1}{2^{2018}}\)
\(2B=\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{2017}}\)
\(2B-B=\left(\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{2017}}\right)-\left(\dfrac{1}{2^3}+\dfrac{1}{2^4}+...+\dfrac{1}{2^{2018}}\right)\)
\(B=\dfrac{1}{2^2}-\dfrac{1}{2^{2018}}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
B = 1/1.6 + 1/6.11 + 1/11.16 + ... + 1/496.501
B x 5 = 5/1.6 + 5/6.11 + 5/11.16 + ... + 5/496.501
B x 5 = 1 - 1/6 + 1/6 - 1/11 + 1/11 - 1/16 + ... + 1/496 - 1/501
B x 5 = 1 - 1/501
B x 5 = 500/501
B = 500/501 : 5
B = 100/501