![](https://rs.olm.vn/images/avt/0.png?1311)
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
A=55/11.16+55/16.21+...+55/36.41
A=11x(1/11−1/16+1/16−1/21+...+1/36−1/41)
A=11x(1/11−1/41)
A=11x30/451
A=30/41
![](https://rs.olm.vn/images/avt/0.png?1311)
Lời giải:
Gọi tổng trên là $A$.
$A=11\times (\frac{5}{11\times 16}+\frac{5}{16\times 21}+\frac{5}{21\times 26}+....+\frac{5}{36\times 41})$
$=11\times (\frac{16-11}{11\times 16}+\frac{21-16}{16\times 21}+\frac{26-21}{21\times 26}+....+\frac{41-36}{36\times 41})$
$=11\times (\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{36}-\frac{1}{41})$
$=11\times (\frac{1}{11}-\frac{1}{41})=1-\frac{11}{41}=\frac{30}{41}$
![](https://rs.olm.vn/images/avt/0.png?1311)
55/11 x 16 + 55/16 x 21 + 55/21 x 26 + 55/26 x 31 + 55/31 x 36 + 55/36 x 41
= 55/11 - 55/16 + 5/16 - 5/21 + 5/21 - 55/26 + 55/26 - 55/31 + 55/31 - 55/36 + 55/36 - 55/41
= 55/11 - 55/41
= 150/41
Mình ko ghi lại đề nha !
= 55 x ( 1/11 x 16 + 1/16 x 21 + 1/21 x 26 + 1/26 x 31 + 1/31 x 36 + 1/36 x 41 )
Vì 1/11 x 16 = 1/1 - 1/11 x 16
=> 1/11 x 21 = 1/231 =1/11 x 16 - 1/16 x 21
....................................................................................
Nếu ta có thể viết :
khúc này viết lại đề bài
= 55 x ( 1/1 - 1/176 + 1/176 -1/336+1/336 - ........................cho đén hết
=55 x ( 1/1 - 1/1476 ) = 55 x 1475/1476 = kết quả tự tính
nhớ
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{55}{11\cdot16}+\frac{55}{16\cdot21}+\frac{55}{21\cdot26}+...+\frac{55}{36\cdot41}\)
\(=\frac{55}{5}\cdot\left(\frac{16-11}{11\cdot16}+\frac{21-16}{16\cdot21}+\frac{26-21}{21\cdot26}+...+\frac{41-36}{36\cdot41}\right)\)
\(=11\cdot\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{26}-\frac{1}{31}+...+\frac{1}{36}-\frac{1}{41}\right)\)
\(=11\cdot\left(\frac{1}{11}-\frac{1}{41}\right)=11\cdot\frac{41-11}{11\cdot41}=\frac{30}{41}\).
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
31 x 55 + 31 x 55 = 1705 + 1705
= 3410
31 x 55 + 31 x 55 = ( 31 x 55 ) + ( 31 x 55 )
= 1705 + 1705
= 3410
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}+\dfrac{1}{28}+\dfrac{1}{36}+\dfrac{1}{45}+\dfrac{1}{55}\)
\(A=2\times\dfrac{1}{2}\times\left(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}+\dfrac{1}{28}+\dfrac{1}{36}+\dfrac{1}{45}+\dfrac{1}{55}\right)\)
\(A=2\times\left(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}+\dfrac{1}{110}\right)\)
\(A=2\times\left(\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+\dfrac{1}{5\times6}+...+\dfrac{1}{9\times10}+\dfrac{1}{10\times11}\right)\)
\(A=2\times\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{10}-\dfrac{1}{11}\right)\)
\(A=2\times\left(\dfrac{1}{2}-\dfrac{1}{11}\right)\)
\(A=2\times\dfrac{9}{22}\)
\(A=\dfrac{9}{11}\)
A=55*[(1/11*16) * 1/5 + (1/16*21) * 1/5 + (1/21*26) * 1/5 + (1/26*31) * 1/5 + (1/31*36) * 1/5 + (1/36*41) * 1/5 ]
= 55* [ (1/11*16) + (1/16*21) + (1/21*26) + (1/26*31) + (1/31*36) + (1/36*41) ] * 1/5
= 55 * [ 1/11-1/16+1/16-1/21+1/21-1/26+1/26-1/31+1/31-1/36+1/36-1/41) * 1/5
= 55 * ( 1/11 - 1/41 ) * 1/5
= 30/41