A>4/5

ớ chết, mk nhầm, lm lại nha

\(S=\frac{1}{31}+\frac{1}{32}+\frac{1}{33}+...+\frac{1}{60}\)

\(S=\left(\frac{1}{31}+\frac{1}{32}+...+\frac{1}{40}\right)+\left(\frac{1}{41}+\frac{1}{42}+...+\frac{1}{50}\right)+\left(\frac{1}{51}+\frac{1}{52}+...+\frac{1}{60}\right)\)

\(S< \frac{1}{30}.10+\frac{1}{40}.10+\frac{1}{50}.10\)

\(S< \frac{1}{3}+\frac{1}{4}+\frac{1}{5}< \frac{4}{5}\)

=> \(S< \frac{4}{5}\)

\(S=\frac{1}{31}+\frac{1}{32}+\frac{1}{33}+...+\frac{1}{60}\)

\(S< 30.\frac{1}{60}\)

\(S< \frac{1}{2}< \frac{4}{5}\)

\(S< \frac{4}{5}\)

\(S=\frac{1}{31}+\frac{1}{32}+\frac{1}{33}+...+\frac{1}{60}\)

\(=\left(\frac{1}{31}+\frac{1}{32}+...+\frac{1}{40}\right)+\left(\frac{1}{41}+\frac{1}{42}+...+\frac{1}{50}\right)+\left(\frac{1}{51}+\frac{1}{52}+...+\frac{1}{60}\right)\)

\(\Rightarrow S< \frac{1}{30}.10+\frac{1}{40}.10+\frac{1}{50}.10\)

\(S< \frac{1}{3}+\frac{1}{4}+\frac{1}{5}< \frac{4}{5}\)

\(V\text{ậy}:S< \frac{4}{5}\)

(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

\(\text{Có 3 trường hợp có thể xảy ra:}\)

\(A=B\)

\(A< B\)
\(A>B\)

mik cần giải mà 

\(A=\left(\frac{1}{31}+\frac{1}{32}+...+\frac{1}{40}\right)+\left(\frac{1}{41}+\frac{1}{42}+...+\frac{1}{50}\right)+\left(\frac{1}{51}+\frac{1}{52}+...+\frac{1}{60}\right)\)

\(Mà:\frac{1}{31}+\frac{1}{32}+...+\frac{1}{40}>\frac{1}{40}.10=\frac{1}{4}\left(\text{10 số hạng}\right)\)

\(\text{Tương tự}:\frac{1}{41}+\frac{1}{42}+...+\frac{1}{50}>\frac{1}{5}\)

\(\frac{1}{51}+\frac{1}{52}+...+\frac{1}{60}>\frac{1}{6}\)

\(\Rightarrow A>\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\)

\(\Rightarrow A>\frac{37}{60}\)

\(Mà\)\(\frac{1}{4}+\frac{1}{5}+\frac{1}{6}>\frac{3}{5}\)

\(\Rightarrow A>\frac{3}{5}\)

\(A=\left(\frac{1}{31}+\frac{1}{32}+...+\frac{1}{40}\right)+\left(\frac{1}{41}+\frac{1}{42}+...+\frac{1}{50}\right)+\left(\frac{1}{51}+\frac{1}{52}+...+\frac{1}{60}\right)\)

\(\frac{1}{31}+\frac{1}{32}+...+\frac{1}{40}< \frac{1}{31}.10=\frac{10}{30}=\frac{1}{3}\left(\text{10 số hạng}\right)\)

\(\Rightarrow A< \frac{4}{5}\)

\(\Rightarrow\frac{3}{5}< A< \frac{4}{5}\)

\(\text{Mik chỉ pít làm z!!!☺}\)

E = (1/31 +1/32+  1/33 +1/34+ 1/35 +1/36+  1/37 +1/38 + 1/39 +1/40) +

( 1/41 +1/42+  1/43 +1/44+ 1/45 +1/46+  1/47 +1/48 + 1/49 +1/50)+

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

Mà  (1/31 +1/32+  1/33 +1/34+ 1/35 +1/36+  1/37 +1/38 + 1/39 +1/40) < ( 1/31 . 10) = 1/ 3 ( 10 số hạng)

Tương tự :( 1/41 +1/42+  1/43 +1/44+ 1/45 +1/46+  1/47 +1/48 + 1/49 +1/50)<1/4 và

(1/51 +1/52+  1/53 +1/54+ 1/55 +1/56+  1/57 +1/58 + 1/59 +1/60)< 1/5

(1/3 + 1/4 + 1/5 ) < 4/5 ( dpcm)

Ưu ái lắm nha!