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

a, \(\dfrac{5}{6}\) = \(\dfrac{10}{12}\) = \(\dfrac{30}{36}\)                         b, \(\dfrac{40}{16}\) = \(\dfrac{10}{4}\) = \(\dfrac{200}{80}\)

c, \(\dfrac{9}{12}\) = \(\dfrac{3}{4}\) = \(\dfrac{54}{72}\)                        d, \(\dfrac{84}{21}\) = \(\dfrac{28}{7}\) = \(\dfrac{4}{1}\)

\(A=\frac{55}{11\cdot16}+\frac{55}{16\cdot21}+\frac{55}{21\cdot26}+...+\frac{55}{36\cdot41}\)

\(=\frac{55}{5}\cdot\left(\frac{16-11}{11\cdot16}+\frac{21-16}{16\cdot21}+\frac{26-21}{21\cdot26}+...+\frac{41-36}{36\cdot41}\right)\)

\(=11\cdot\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{26}-\frac{1}{31}+...+\frac{1}{36}-\frac{1}{41}\right)\)

\(=11\cdot\left(\frac{1}{11}-\frac{1}{41}\right)=11\cdot\frac{41-11}{11\cdot41}=\frac{30}{41}\).

Lời giải:
Gọi tổng trên là $A$.

$A=11\times (\frac{5}{11\times 16}+\frac{5}{16\times 21}+\frac{5}{21\times 26}+....+\frac{5}{36\times 41})$

$=11\times (\frac{16-11}{11\times 16}+\frac{21-16}{16\times 21}+\frac{26-21}{21\times 26}+....+\frac{41-36}{36\times 41})$

$=11\times (\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{36}-\frac{1}{41})$

$=11\times (\frac{1}{11}-\frac{1}{41})=1-\frac{11}{41}=\frac{30}{41}$

\(\dfrac{55}{11}\cdot6+\dfrac{55}{16}\cdot21+\dfrac{55}{21}\cdot26+\dfrac{55}{26}\cdot31+\dfrac{55}{31}\cdot36+\dfrac{55}{36}\cdot41=30+\dfrac{1155}{16}+\dfrac{1430}{21}+\dfrac{1705}{26}+\dfrac{1980}{31}+\dfrac{2255}{36}=\dfrac{12186720}{406224}+\dfrac{29324295}{406224}+\dfrac{27661920}{406224}+\dfrac{26638920}{406224}+\dfrac{25945920}{406224}+\dfrac{25445420}{406224}=\dfrac{147203195}{406224}\)

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

sai rồi kết quả là 30/41 mới đúng

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

câu 1 = -68

câu 2 =-2500

câu 3=168

câu 4 =4571

câu 6=124

a) \(S4=\frac{3}{50}+\frac{3}{150}+\frac{3}{300}+...+\frac{3}{9500}\)

\(S4=\frac{3}{5.10}+\frac{3}{10.15}+\frac{3}{15.20}+...+\frac{3}{95.100}\)

\(S4=\frac{3}{5}\left(\frac{1}{5}-\frac{1}{10}+\frac{1}{10}-\frac{1}{15}+\frac{1}{15}-\frac{1}{20}+...+\frac{1}{95}-\frac{1}{100}\right)\)

\(S4=\frac{3}{5}\left(\frac{1}{5}-\frac{1}{100}\right)\)

\(S4=\frac{3}{5}.\frac{19}{100}\)

\(S4=\frac{57}{500}\Rightarrow S=\frac{57}{500}:4=\frac{57}{2000}\)

b) \(S5=\frac{55}{11.16}+\frac{55}{16.21}+...+\frac{55}{36.41}\)

\(S5=\frac{55}{5}.\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{36}-\frac{1}{41}\right)\)

\(S5=11.\left(\frac{1}{11}-\frac{1}{41}\right)\)

\(S5=11.\frac{30}{451}\)

\(S5=\frac{30}{41}\Rightarrow S=\frac{30}{41}:5=\frac{6}{41}\)

Mình không hiểu ý bạn là S.4 hay là S4 là tên