B 

trừ a,c,d ra :)))

49

49

Ta có:

55/11x16+55/16x21+55/21x26x.....x55/36x41

=55/5 x (1/11-1/16+1/16-1/21+.......+1/36-1/41)

=55/5 x (1/11-1/41)

=55/5x30/451

=30/41

nhớ ****

A=55/11.16+55/16.21+55/21.26+55/26.31+55/31.36+55/36.41

  =11.(5/11.16+5/16.21+...+5/36.41)

  =11.(1/11-1/16+1/16-1/21+...+1/36-1/41)

  =11.(1/11-1/41)

  =11.30/451

  =30/41

sao biết đúng

= 275 + 55 + 55 x .... =  3025

=  330 + 55 x .... = 3025

 55 x ... = 3025 -330

55 x ... = 29695

 ....= 29695 : 55

..... =  539,9.... ( nếu là toán lớp 4 thì đề sai nhé )

Lời giải:
Gọi tổng trên là $A$.

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

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

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

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

\(=11\left(\dfrac{5}{6\cdot11}+\dfrac{5}{11\cdot16}+\dfrac{5}{16\cdot21}+\dfrac{5}{21\cdot26}+\dfrac{5}{26\cdot31}\right)\)

=11(1/6-1/11+1/11-1/16+1/16-1/21+1/21-1/26+1/26-1/31)

=11*25/186=275/186

\(\dfrac{55}{6x11}+\dfrac{55}{11x16}+\dfrac{55}{21x16}+\dfrac{55}{21x26}+\dfrac{55}{31x26}\)

\(=55\left(\dfrac{1}{6x11}+\dfrac{1}{11x16}+\dfrac{1}{21x16}+\dfrac{1}{21x26}+\dfrac{1}{31x26}\right)\)

\(=55\left(\dfrac{1}{5}x\left(\dfrac{1}{6}-\dfrac{1}{11}\right)+\dfrac{1}{5}x\left(\dfrac{1}{11}-\dfrac{1}{16}\right)+\dfrac{1}{5}x\left(\dfrac{1}{16}-\dfrac{1}{21}\right)+\dfrac{1}{5}x\left(\dfrac{1}{21}-\dfrac{1}{26}\right)+\dfrac{1}{5}x\left(\dfrac{1}{26}-\dfrac{1}{31}\right)\right)\)

\(=55x\dfrac{1}{5}x\left(\dfrac{1}{6}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{31}\right)\)

\(=11x\left(\dfrac{1}{6}-\dfrac{1}{31}\right)=11x\left(\dfrac{31-6}{186}\right)=11x\dfrac{25}{186}=\dfrac{275}{186}\)

C=\(\dfrac{55}{6\cdot11}\)+\(\dfrac{55}{11\cdot16}\)+\(\dfrac{55}{16\cdot21}\)+\(\dfrac{55}{21\cdot26}\)+\(\dfrac{55}{26\cdot31}\)

 =\(\dfrac{1}{6}\)-\(\dfrac{1}{11}\)+\(\dfrac{1}{11}\)-\(\dfrac{1}{16}\)+\(\dfrac{1}{16}\)-\(\dfrac{1}{21}\)+\(\dfrac{1}{21}\)-\(\dfrac{1}{26}\)+\(\dfrac{1}{26}\)-\(\dfrac{1}{31}\)

 =\(\dfrac{1}{6}\)-\(\dfrac{1}{31}\)=\(\dfrac{25}{186}\)

\(\frac{A}{11}=\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+\frac{5}{26.31}+\frac{5}{31.36}+\frac{5}{36.41}\)

\(\frac{A}{11}=\frac{16-11}{11.16}+\frac{21-16}{16.21}+\frac{26-21}{21.26}+...+\frac{41-36}{36.41}\)

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

\(\frac{A}{11}=\frac{1}{11}-\frac{1}{41}=\frac{30}{11.41}\Rightarrow A=\frac{11.30}{11.41}=\frac{30}{41}\)

\(\sqrt[1]{\dfrac{2}{3}_3\dfrac{1}{2}3_3\dfrac{3}{4}^3}\)