Cho S= \(\frac{5}{20}\)+ \(\frac{5}{21}\)+ \(\frac{5}{22}\)+ \(\frac{5}{23}\) + \(\frac{5}{24}\)
Chứng minh S < 1
Mình cần gấp lắm. Giải nhanh mình tick cho ( phải có cách giải )
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)
M= \(\frac{5}{20}\)+\(\frac{5}{21}\)+\(\frac{5}{22}\)+\(\frac{5}{23}\)+\(\frac{5}{24}\)
chứng minh M >1
Do \(\frac{5}{20}>\frac{5}{21};\frac{5}{21}>\frac{5}{22};\frac{5}{22}>\frac{5}{23};\frac{5}{23}>\frac{5}{24}\)
Mà \(\frac{5}{24}>\frac{5}{25}\)
\(\Rightarrow\frac{5}{20}+\frac{5}{21}+\frac{5}{22}+\frac{5}{23}+\frac{5}{24}>\frac{5}{25}+\frac{5}{25}+\frac{5}{25}+\frac{5}{25}+\frac{5}{25}=5.\frac{5}{25}=1\)
Vậy M > 1
Ai thấy đúng k nha
Cho tổng \(S=\frac{1}{5^2}+\frac{1}{5^4}+\frac{1}{5^6}+\frac{1}{5^8}+...+\frac{1}{5^{2014}}\)
Chứng minh \(S
S=5/20+5/21+5/22+5/23+5/24 HÃY CHỨNG MINH S>1
Ta có: \(\frac{5}{20}>\frac{5}{25}\)
\(\frac{5}{21}>\frac{5}{25}\)
\(\frac{5}{22}>\frac{5}{25}\)
\(\frac{5}{23}>\frac{5}{25}\)
\(\frac{5}{24}>\frac{5}{25}\)
=> \(S>\frac{5}{25}+\frac{5}{25}+\frac{5}{25}+\frac{5}{25}+\frac{5}{25}=5\cdot\frac{5}{25}=\frac{25}{25}=1\)
Vậy S > 1
Ta có :
\(\frac{5}{20}>\frac{5}{25}\)
\(\frac{5}{21}>\frac{5}{25}\)
\(\frac{5}{22}>\frac{5}{25}\)
\(\frac{5}{23}>\frac{5}{25}\)
\(\frac{5}{24}>\frac{5}{25}\)
\(\Rightarrow S>\frac{5}{25}+\frac{5}{25}+\frac{5}{25}+\frac{5}{25}+\frac{5}{25}=5\cdot\frac{5}{25}=\frac{25}{25}=1\)
Vậy \(S>1\)
Chứng minh:
S= 5/20 + 5/21 + 5/22 + 5/23 + 5/24 > 1
Ta có :
\(\frac{5}{20}>\frac{5}{25}\)
\(\frac{5}{21}>\frac{5}{25}\)
\(\frac{5}{22}>\frac{5}{25}\)
\(\frac{5}{23}>\frac{5}{25}\)
\(\frac{5}{24}>\frac{5}{25}\)
\(\Rightarrow\frac{5}{20}+\frac{5}{21}+\frac{5}{22}+\frac{5}{23}+\frac{5}{24}>5.\frac{5}{25}=1\)
\(\Rightarrow\frac{5}{20}+\frac{5}{21}+\frac{5}{22}+\frac{5}{23}+\frac{5}{24}>1\)
ta có S=5/20+5/21+5/22+5/23+5/24>5/25+5/25+5/25+5/25+5/25=5/25*5=1
=>đpcm
Cho S =\(\frac{5}{20}+\frac{5}{21}+\frac{5}{22}+...+\frac{5}{49}\). Chứng minh : 3<S<8
Cho tổng S = \(\frac{1}{5^2}+\frac{1}{5^4}+\frac{1}{5^6}+\frac{1}{5^8}+...+\frac{1}{5^{2014}}\)
Chứng minh S < \(\frac{1}{24}\)
ko can biet: làm đc mk làm lâu r :<
\(\frac{S}{25}=\frac{1}{5^4}+\frac{1}{5^6}+\frac{1}{5^8}+....+\frac{1}{5^{2016}}\)
\(S-\frac{S}{25}=\frac{1}{5^2}-\frac{1}{5^{2016}}<\frac{1}{5^2}\)
\(\frac{24S}{25}<\frac{1}{25}\)=> dpcm
Cho S= \(\frac{5}{20}+\frac{5}{21}+...+\frac{5}{49}.\)Chứng tỏ rằng 3< S < 8
Ta có \(S=5.\left(\frac{1}{20}+\frac{1}{21}+...+\frac{1}{49}\right)\)
\(S>5.\left(\frac{1}{49}+\frac{1}{49}+...+\frac{1}{49}\right)\)30 số hạng
\(S>5.\frac{30}{49}\)
\(S>\frac{150}{49}\)
\(S>3\frac{3}{49}\)
Suy ra \(S
Ta có:\(S< \frac{5}{20}+\frac{5}{20}+\frac{5}{20}+...+\frac{5}{20}\)(30 số hạng)
\(=\frac{150}{20}< 8\)
\(\Rightarrow S< 8\left(1\right)\)
Ta lại có:\(S>\frac{5}{50}+\frac{5}{50}+\frac{5}{50}+...+\frac{5}{50}\)(30 số hạng)
\(=\frac{150}{50}=3\)
\(\Rightarrow\)S<3(2)
từ (1) và (2) suy ra điều phải chứng minh
hàng thật nha các bạn không copy nhe!
S = 5/20 + 5/21 + 5/22 + 5/23 + 5/24
tính giá trị biểu thức và chứng minh S > 1
Giải:
Ta có:
\(\dfrac{5}{20}>\dfrac{5}{25}\) ; \(\dfrac{5}{21}>\dfrac{5}{25}\) ;\(\dfrac{5}{22}>\dfrac{5}{25}\) ; \(\dfrac{5}{23}>\dfrac{5}{25}\) ; \(\dfrac{5}{24}>\dfrac{5}{25}\)
\(\Rightarrow S=\dfrac{5}{20}+\dfrac{5}{21}+\dfrac{5}{22}+\dfrac{5}{23}+\dfrac{5}{24}>\dfrac{5}{25}+\dfrac{5}{25}+\dfrac{5}{25}+\dfrac{5}{25}+\dfrac{5}{25}=1\)
Vậy \(S=\dfrac{5}{20}+\dfrac{5}{21}+\dfrac{5}{22}+\dfrac{5}{23}+\dfrac{5}{24}>1\) ( đpcm )
Giải:
Dễ thấy:
\(20< 25\Leftrightarrow\dfrac{5}{20}>\dfrac{5}{25}\)
\(21< 25\Leftrightarrow\dfrac{5}{21}>\dfrac{5}{25}\)
\(.....................\)
\(24< 25\Leftrightarrow\dfrac{5}{24}>\dfrac{5}{25}\)
Cộng vế theo vế ta có:
\(S>\dfrac{5}{25}+\dfrac{5}{25}+...+\dfrac{5}{25}=\dfrac{5}{25}.5=\dfrac{25}{25}=1\)
Vậy \(S>1\) (Đpcm)
\(S=\dfrac{5}{20}+\dfrac{5}{21}+\dfrac{5}{22}+\dfrac{5}{23}+\dfrac{5}{24}>\dfrac{5}{25}+\dfrac{5}{25}+\dfrac{5}{25}+\dfrac{5}{25}+\dfrac{5}{25}=1\)
\(\Rightarrow S>1\)
