Ta thấy : \(\frac{5}{11}>\frac{5}{12}>\frac{5}{13}>\frac{5}{14}\)

 \(S=\frac{5}{11}+\frac{5}{12}+\frac{5}{13}+\frac{5}{14}< \frac{5}{11}\times4=\frac{20}{11}< 2\)  (1)

\(S=\frac{5}{11}+\frac{5}{12}+\frac{5}{13}+\frac{5}{14}>\frac{5}{14}\times4=\frac{10}{7}>1\)   (2)

Từ (1) và (2) suy ra : \(1< S< 2\)  (ĐPCM)

Sửa đề : Chứng minh : S > 1

Ta thấy : \(\frac{5}{20}>\frac{5}{21}>\frac{5}{22}>\frac{5}{23}>\frac{5}{24}\)

\(\Rightarrow S=\frac{5}{20}+\frac{5}{21}+\frac{5}{22}+\frac{5}{23}+\frac{5}{24}>\frac{5}{24}\times5=\frac{25}{24}>1\)

Vậy S > 1 (ĐPCM)

\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+.....+\frac{1}{59\cdot60}\)

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

\(=1-\frac{1}{60}\)

\(=\frac{59}{60}\)

X=59/60 nha

Ta có : \(\frac{12x+1}{2x+3}=\frac{12x+18-17}{2x+3}=\frac{6\left(2x+3\right)-17}{2x+3}=6-\frac{17}{2x+3}\)

Vì \(6\inℤ\Rightarrow\frac{12x+1}{2x+3}\inℤ\Leftrightarrow\frac{17}{2x+3}\inℤ\Rightarrow17⋮2x+3\Rightarrow2x+3\inƯ\left(17\right)\)

=> \(2x+3\in\left\{1;17;-1;-17\right\}\Rightarrow x\in\left\{-1;7;-2;-10\right\}\)

\(\frac{x}{7}=\frac{-y}{4}=\frac{-8}{z}=\frac{-28}{49}\)

Cái này thì phải làm ngược từ phải sang trái =))

* \(\frac{-8}{z}=\frac{-28}{49}\Leftrightarrow-28z=-8\cdot49\Leftrightarrow-28z=-392\Leftrightarrow z=14\)

* \(\frac{-y}{4}=\frac{-8}{14}\Leftrightarrow-14y=-8\cdot4\Leftrightarrow-14y=-32\Leftrightarrow y=\frac{16}{7}\)

* \(\frac{x}{7}=\frac{-\frac{16}{7}}{4}\Leftrightarrow4x=-\frac{16}{7}\cdot7\Leftrightarrow4x=-16\Leftrightarrow x=-4\)

\(\frac{x}{7}=\frac{-y}{4}=\frac{-8}{z}=\frac{-28}{49}\)

\(\Rightarrow\frac{x}{7}=\frac{-28}{49};\frac{-y}{4}=\frac{-28}{49};\frac{-8}{z}=\frac{-28}{49}\)

+)\(\frac{x}{7}=\frac{-28}{49}\Rightarrow49x=\left(-28\right).7\Rightarrow49x=-196\Rightarrow x=\frac{-196}{49}=-4\)

+)\(\frac{-y}{4}=\frac{-28}{49}\Rightarrow-49y=\left(-28\right).4\Rightarrow-49y=-112\Rightarrow y=\frac{-112}{49}\)

+)\(\frac{-8}{z}=\frac{-28}{49}\Rightarrow-28z=49.\left(-8\right)\Rightarrow-28z=-392\Rightarrow z=\frac{-392}{-28}=14\)

Vậy x=-4;y=\(\frac{-112}{49}\);z=14

Chúc bạn học tốt

a) \(H=\left\{x\inℕ|5< \frac{x}{2}< 11|\frac{x}{2}\inℕ\right\}\)

b) \(K=\left\{x\inℕ|4< \frac{x-1}{2}< 12|\frac{x-1}{2}\inℕ\right\}\)

c) Thiếu ngoặc rồi nghen

s g