\(A=\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{2016.2017}\right):2\)

\(=\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2016}-\frac{1}{2017}\right):2\)

\(=\left(1-\frac{1}{2017}\right):2\)\(< \)\(\frac{1}{2}\)   (Do 1 - 1/2017 < 1)

B = 1/1.2 + 1/3.4 + 1/5.6 + ... + 1/59.60

B = 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + ... + 1/59 - 1/60

B = (1 + 1/3 + 1/5 + ... + 1/59) - (1/2 + 1/4 + 1/6 + ... + 1/60)

B = (1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + ... + 1/59 + 1/60) - 2.(1/2 + 1/4 + 1/6 + ... + 1/60)

B = (1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + ... + 1/59 + 1/60) - (1 + 1/2 + 1/3 + ... + 1/30)

B = 1/31 + 1/32 + 1/33 + ... + 1/60 = A

=> B = A

ta có: Lớn nhất của A là:\(\frac{1}{31}+\frac{1}{31}+...+\frac{1}{31}\)(30 phân số)

         =30/31

  B=1-\(\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{3}+...+\frac{1}{59}-\frac{1}{60}\)\(=\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{59}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{60}\right)\)

Bé nhất của của B là :\(\left(1+1+...+1\right)-\left(\frac{1}{60}+\frac{1}{60}+...+\frac{1}{60}\right)\)

                                \(=30-\frac{30}{60}\)

=>B>A

ai trả lời đúng mình tặng coin

S = (1/31+1/32+1/33+...+1/40) + (1/41 + 1/42 + ...+ 1/50) + (1/51 + 1/52+...+1/59+1/60)

Mà : (1/31+1/32+1/33+...+1/40) > 1/40 x 10 = 1/4 (gồm 10 số hạng)

Tương tự : (1/41 + 1/42 + ...+ 1/50) > 1/5 ;   (1/51 + 1/52+...+1/59+1/60) > 1/6

S > 1/4 + 1/5 + 1/6.

Trong khi đó (1/4 + 1/5 + 1/6) > 3/5

=>S > 3/5                             (1)

S = (1/31+1/32+1/33+...+1/40) + (1/41 + 1/42 + ...+ 1/50) + (1/51 + 1/52+...+1/59+1/60)

Mà : (1/31+1/32+1/33+...+1/40) < 1/31 x 10 = 10/30 = 1/3 (gồm 10 số hạng)

=> S <  4/5                             (2)

Từ (1) và (2) => 3/5 <S<4/5

(1/51 +1/52+  1/53 +1/54+ 1/55 +1/56+  1/57 +1/58 + 1/59 +1/60)(1/51 +1/52+  1/53 +1/54+ 1/55 +1/56+  1/57 +1/58 + 1/59 +1/60)(1/51 +1/52+  1/53 +1/54+ 1/55 +1/56+  1/57 +1/58 + 1/59 +1/60)(1/51 +1/52+  1/53 +1/54+ 1/55 +1/56+  1/57 +1/58 + 1/59 +1/60)(1/51 +1/52+  1/53 +1/54+ 1/55 +1/56+  1/57 +1/58 + 1/59 +1/60)(1/51 +1/52+  1/53 +1/54+ 1/55 +1/56+  1/57 +1/58 + 1/59 +1/60)(1/51 +1/52+  1/53 +1/54+ 1/55 +1/56+  1/57 +1/58 + 1/59 +1/60)(1/51 +1/52+  1/53 +1/54+ 1/55 +1/56+  1/57 +1/58 + 1/59 +1/60)(1/51 +1/52+  1/53 +1/54+ 1/55 +1/56+  1/57 +1/58 + 1/59 +1/60)(1/51 +1/52+  1/53 +1/54+ 1/55 +1/56+  1/57 +1/58 + 1/59 +1/60)(1/51 +1/52+  1/53 +1/54+ 1/55 +1/56+  1/57 +1/58 + 1/59 +1/60)

E = 1/31+1/32+...+1/60

E > 1/40+1/40+...+1/40+1/41+1/42+...+1/60

E > 20/40+1/41+1/42+...+1/60

E > 1/2+1/60+1/60+...+1/60

E > 1/2 + 1/3 = 5/6

Mà 5/6 > 4/5

=> E > 4/5