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

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

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

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

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

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

trả lời cho mình nha mình k cho

\(\frac{29}{68}\times\frac{31}{55}+\frac{31}{68}\times\frac{26}{55}=\frac{31}{68}\times\frac{29}{55}+\frac{31}{68}\times\frac{26}{55}\)

                                                    \(=\frac{31}{68}\times\left(\frac{29}{55}+\frac{26}{55}\right)\)

                                                    \(=\frac{31}{68}\)

\(\frac{29}{68}.\frac{31}{55}+\frac{31}{68}.\frac{26}{55}\)

\(=\frac{29}{68}.\frac{31}{55}+\frac{26}{68}.\frac{31}{55}\)

\(=\left(\frac{29}{68}+\frac{26}{68}\right).\frac{31}{55}\)

\(=\frac{55}{68}.\frac{31}{55}\)

\(=\frac{31}{68}\)

Học tốt

(26 x 27 + 26 x 73) x (30 x 31 - 30) x (34 x 110 - 55 x 68) x (55 x 68 + 55 x 32)

= [26 x (27 + 73)] x [30 x (31 - 1) x (34 x 55 x 2 - 55 x 68) x [55 x (68 + 32)

= (26 x 100) x (30 x 30) x [68 x 55 - 55 x 68) x (55 x 100)

= 2600 x 900 x (68 x (55 - 55) x 5500

= 2600 x 900 x (68 x 0) x 5500

= 2600 x 900 x 0 x 5500

= 0

vì 0 nhân với số nào cũng bằng 0

bạn giỏi quá,mình có thể kết bạn với bạn được ko?

[(x.x + 55) - 31].14 = 560

x² + 55 - 31 = 560 : 14

x² + 24 = 40

x² = 40 - 24

x² = 16

x = 4 hoặc x = -4

\(\left[\left(x\cdot x+55\right)-31\right]\cdot14=560\)

=>\(\left(x^2+55-31\right)=40\)

=>\(x^2=16\)

=>\(\left[{}\begin{matrix}x=4\\x=-4\end{matrix}\right.\)