Lời giải:
Gọi tổng trên là $A$.

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

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

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

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

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

\(\frac{5}{11.16}+\frac{5}{16.21}+..+\frac{5}{36.41}\)

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

\(=\frac{1}{11}-\frac{1}{41}\)

= bn tự timnhs nha......................................

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\(\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{36.41}\)

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

\(=\frac{1}{11}-\frac{1}{41}\)

\(=\frac{30}{451}\)

_Chúc bạn học tốt_

\(A=\frac{5}{11\times16}+\frac{5}{16\times21}+....+\frac{5}{36\times41}.\)

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

\(A=\frac{1}{11}-\frac{4}{41}=\frac{30}{451}\)

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