Question

Cho S= 1/21+1/22+...+1/35. Chứng minh rằng S>1/2

Answer 1

Easy!!

\(S=\dfrac{1}{21}+\dfrac{1}{22}+...+\dfrac{1}{35}>\dfrac{1}{29}+\dfrac{1}{29}+...+\dfrac{1}{29}\) (15 phân số \(\dfrac{1}{29}\))

\(=\dfrac{1.15}{29}=\dfrac{15}{29}>\dfrac{1}{2}\) (*)

\(\Rightarrow\dfrac{1}{21}+\dfrac{1}{22}+...+\dfrac{1}{35}>\dfrac{1}{2}^{\left(đpcm\right)}\)

P/s: đpcm là điều phải chứng minh

Answer 2

Có \(S=\dfrac{1}{21}+\dfrac{1}{22}+......+\dfrac{1}{35}\)

\(S=\dfrac{1}{21}+\dfrac{1}{22}+.........+\dfrac{1}{35}>\dfrac{1}{29}+\dfrac{1}{29}+\dfrac{1}{29}+........+\dfrac{1}{29}\)( 15 phân số \(\dfrac{1}{29}\))

\(S=\dfrac{15}{29}>\dfrac{1}{2}\)

\(S>\dfrac{1}{2}\)

Vậy S > \(\dfrac{1}{2}\)(đpcm)