\(\Rightarrow A=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+.....+\frac{1}{26}-\frac{1}{31}\)

\(\Rightarrow A=1-\frac{1}{31}\)

\(\Rightarrow A=\frac{30}{31}\)

\(A=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{26.31}\)

\(=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{26}-\frac{1}{31}\)

\(=1+\left(-\frac{1}{6}+\frac{1}{6}\right)+\left(-\frac{1}{11}+\frac{1}{11}\right)+...+\left(-\frac{1}{26}+\frac{1}{26}\right)-\frac{1}{31}\)

\(=1-\frac{1}{31}=\frac{31-1}{31}=\frac{30}{31}\)

\(\text{Vậy }A=\frac{30}{31}\).

A = \(\frac{5}{1x6}+\frac{5}{6x11}+\frac{5}{11x16}+...+\frac{5}{26x31}\)

A=  \(\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{26}-\frac{1}{31}\)

A = \(\frac{1}{1}-\frac{1}{31}=\frac{31}{31}-\frac{1}{31}=\frac{30}{31}\)

Ta có:

B = 10/1.6 + 10/6.11 + 10/11.16 + ... + 10/46.51

B = 2(5/1.6 + 5/6.11 + 5/11.16 + ... + 5/46.51)

B = 2 . (1 - 1/6 + 1/6 - 1/11 + 1/11 - 1/16 + ... + 1/46 - 1/51)

B = 2. (1 - 1/51)

B = 2.50/51

B = 100/51 < 102/51 = 2

=> Ta có đpcm

\(B=\dfrac{10}{1.6}+\dfrac{10}{6.11}+\dfrac{10}{11.16}+.....+\dfrac{10}{46.51}\)

\(B=2\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+.....+\dfrac{1}{46}-\dfrac{1}{51}\right)\)

\(B=2\left(1-\dfrac{1}{51}\right)\)

\(B=2-\dfrac{2}{51}\)

\(B< 2\left(đpcm\right)\)

\(A=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{1}{26.31}\)

    \(=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}+...+\frac{1}{26}-\frac{1}{31}\)

    \(=1+\left(-\frac{1}{6}+\frac{1}{6}\right)+\left(-\frac{1}{11}+\frac{1}{11}\right)+...+\left(-\frac{1}{26}+\frac{1}{26}\right)-\frac{1}{31}\)

 \(=1-\frac{1}{31}=\frac{31-1}{31}\)

\(=\frac{30}{31}\)

Vậy \(A=\frac{30}{31}\)

\(A=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{26.31}\)

\(\Rightarrow A=\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{26}-\frac{1}{31}\)

\(\Rightarrow A=\frac{1}{1}-\frac{1}{31}\)

\(\Rightarrow A=\frac{30}{31}\)

28,37-23,18-16,82+71,63
=(28,37+71,63)-(23,18+16,82)

=60

B=1/1x6 + 1/6x11 + 1/16x21 + 1/21x26 + 1/26x31

=1-1/6+1/6-1/11+1/11-....-1/31

=1-1/31=30/31

a) A = \(\left(28,37+71,63\right)-\left(23,18+16,82\right)\)

= 100 - 40

= 60

b) \(B=\dfrac{1}{1.6}+\dfrac{1}{6.11}+\dfrac{1}{11.16}+\dfrac{1}{16.21}+\dfrac{1}{21.26}+\dfrac{1}{26.31}\)

= \(\dfrac{1}{5}\left(\dfrac{5}{1.6}+\dfrac{5}{6.11}+...+\dfrac{5}{26.31}\right)\)

= \(\dfrac{1}{5}\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{26}-\dfrac{1}{31}\right)\)

= \(\dfrac{1}{5}\left(1-\dfrac{1}{31}\right)=\dfrac{1}{5}.\dfrac{30}{31}=\dfrac{6}{31}\)

28,37-23,18-16,82+71,63 

= (28,37 + 71,63) - (23,18 + 16,82)

= 110 - 40

= 70

Chúc bạn học tôt.

\(\frac{5^2}{1.6}+\frac{5^2}{6.11}+...+\frac{5^2}{26.31}\)

\(=5\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{26.31}\right)\)

\(=5\left(\frac{6-1}{1.6}+\frac{11-6}{6.11}+...+\frac{31-26}{26.31}\right)\)

\(=5\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{26}-\frac{1}{31}\right)\)

\(=5\left(1-\frac{1}{31}\right)=\frac{150}{31}\)

ủng hộ mình lên 330 điểm nha các bạn

\(\frac{1}{1.6}+\frac{1}{6.11}+...+\frac{1}{96.101}\)

\(=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{96}-\frac{1}{101}\)

\(=1-\frac{1}{101}\)

\(=\frac{100}{101}\)

đặt biểu thức là A

5A=(1/1x6+1/6x11+...+1/96x101)x5=5/1x6+5/6x11+...+5/96x101

5A=6-1/1x6+11-6/6x11+...+101-96/96x101

5A=6/1x6-1/1x6+11/6x11-6/6x11+...+101/96x101-96/96x101

5A=1-1/6+1/6-1/11+...+1/96-1/101(sau khi rút gọn các phân số)

5A=1-1/101(còn lại sau khi trừ)

5A=100/101

A=100/101:5=20/101