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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
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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)
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
![](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)
\(\frac{4}{7}.\frac{5}{36}.\frac{21}{25}\)
\(=\frac{4.5.21}{7.36.25}\)
\(=\frac{4.5.7.3}{7.4.9.5.5}\)
\(=\frac{3}{9.5}=\frac{3}{3.3.5}=\frac{1}{15}\)
\(\frac{25}{28}:\frac{15}{14}.\frac{6}{7}\)
\(=\frac{25.14.6}{28.15.7}\)
\(=\frac{5.5.14.6}{28.5.3.7}\)
\(=\frac{5.6}{2.3.7}=\frac{5.2.3}{2.3.7}\)
\(=\frac{5}{7}\)
\(\frac{\left(\frac{36}{41}:\frac{9}{41}\right)}{\left(\frac{14}{21}:\frac{7}{21}\right)}\times\frac{2}{5}\)
\(=\frac{\left(\frac{36}{41}\times\frac{41}{9}\right)}{\left(\frac{14}{21}\times\frac{21}{7}\right)}\times\frac{2}{5}\)
\(=\frac{4}{2}\times\frac{2}{5}\)
\(=\frac{4}{5}\)
~ Ủng hộ nhé
\(\frac{\text{36/41 : 9/41 }}{\text{14/21: 7/21}}\)= \(\frac{4}{2}\)= 2 => 2 x \(\frac{2}{5}\)= \(\frac{4}{5}\)