a)Cho A= 3/10+3/11+3/12+3/13+3/14.
Chứng minh A<3/2
b)Cho B=1/11+1/12+1/13+....+1/20.
Chứng minh 7/12<B<5/6c
c)Cho C=1/5+1/6+....+1/17
Chứng minh C>1
Cho A= 3/10 + 3/11 + 3/12 + 3/13 + 3/14. Chứng minh rằng: 1 < A < 2
cho A=3/10 + 3/11 + 3/12 + 3/13 + 3/14
chứng minh rằng 1<A<2 từ đó suy ra A ko phải là số tự nhiên
vi 3/10>3/15
3/11>3/15
...........
3/14>3/15
cong ve ta duoc
3/10+3/11+...+3/14>3/15.5=1(1)
vi 3/10<3/9
3/11<3/9
..............
3/14<3/9
cong ve ta duoc
3/10+3/11+...+3/14<3/9.5=5/3<2(2)
tu (1)va(2)
=>1<A<2
=>A khong phai la so tu nhien
Cho A = 3/10 + 3/11 + 3/12 + 3/13 + 3/14
Chứng tỏ 1 < A < 2
Cho \(A=\frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}\). Chứng minh rằng : 1 < A < 2.
giúp mình với
S=\(\frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}<\frac{4}{10}+\frac{4}{10}+\frac{4}{10}+\frac{4}{10}+\frac{4}{10}\)
=\(\frac{4}{10}\cdot5=2=>S<2\)
S=\(\frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}<\frac{3}{15}+\frac{3}{15}+\frac{3}{15}+\frac{3}{15}+\frac{3}{15}\)
=\(\frac{3}{15}\cdot5=1=>S>1\)
Vậy 1<S<2
nhớ k với nhé
Cho S = 3/10 + 3/11+3/12+3/13+3/14 . Chứng minh rằng 1 nhỏ hơn S nhỏ hơn 2
Cho S = 3/10 + 3/11+3/12+3/13+3/14 . Chứng minh rằng 1 nhỏ hơn S nhỏ hơn 2
\(S=\dfrac{3}{10}+\dfrac{3}{11}+\dfrac{3}{12}+\dfrac{3}{13}+\dfrac{3}{14}\)
\(\Rightarrow S< \dfrac{3}{10}+\dfrac{3}{10}+\dfrac{3}{10}+\dfrac{3}{10}+\dfrac{3}{10}\)
\(\Rightarrow S< \dfrac{15}{10}< 2\)
Lại có \(S>\dfrac{3}{14}+\dfrac{3}{14}+\dfrac{3}{14}+\dfrac{3}{14}+\dfrac{3}{14}\)
\(\Rightarrow S>\dfrac{15}{14}>1\)
\(\Rightarrow1< S< 2\)
Cho S= \(\dfrac{3}{10}+\dfrac{3}{11}+\dfrac{3}{12}+\dfrac{3}{13}+\dfrac{3}{14}\)
Chứng minh rằng: 1<S<2
Ta có: \(\dfrac{3}{10}>\dfrac{3}{15}\)
\(\dfrac{3}{11}>\dfrac{3}{15}\)
\(\dfrac{3}{12}>\dfrac{3}{15}\)
\(\dfrac{3}{13}>\dfrac{3}{15}\)
\(\dfrac{3}{14}>\dfrac{3}{15}\)
Do đó: \(\dfrac{3}{10}+\dfrac{3}{11}+\dfrac{3}{12}+\dfrac{3}{13}+\dfrac{3}{14}>\dfrac{3}{15}+\dfrac{3}{15}+\dfrac{3}{15}+\dfrac{3}{15}+\dfrac{3}{15}=1\)
hay 1<S(1)
Ta có: \(\dfrac{3}{11}< \dfrac{3}{10}\)
\(\dfrac{3}{12}< \dfrac{3}{10}\)
\(\dfrac{3}{13}< \dfrac{3}{10}\)
\(\dfrac{3}{14}< \dfrac{3}{10}\)
Do đó: \(\dfrac{3}{11}+\dfrac{3}{12}+\dfrac{3}{13}+\dfrac{3}{14}< \dfrac{3}{10}+\dfrac{3}{10}+\dfrac{3}{10}+\dfrac{3}{10}=\dfrac{12}{10}\)
\(\Leftrightarrow S< \dfrac{15}{10}=\dfrac{3}{2}< 2\)(2)
Từ (1) và (2) suy ra 1<S<2(đpcm)
cho S=(3)/(10)+(3)/(11)+(3)/(12)+(3)/(13)+(3)/(14). chứng minh rằng S không là số tự nhiên
Cho S=3/10+3/11+3/12+3/13+3/14 Chứng minh:1<S<2
\(S=\dfrac{3}{10}+\dfrac{3}{11}+\dfrac{3}{12}+\dfrac{3}{13}+\dfrac{3}{14}\)
Ta thấy:
\(\dfrac{3}{10}>\dfrac{3}{15}\\\dfrac{3}{11}>\dfrac{3}{15}\\ \dfrac{3}{12}>\dfrac{3}{15}\\ \dfrac{3}{13}>\dfrac{3}{15}\\ \dfrac{3}{14}>\dfrac{3}{15} \)
\(\Rightarrow S=\dfrac{3}{10}+\dfrac{3}{11}+\dfrac{3}{12}+\dfrac{3}{13}+\dfrac{3}{14}>5\cdot\dfrac{3}{15}\\ S=\dfrac{3}{10}+\dfrac{3}{11}+\dfrac{3}{12}+\dfrac{3}{13}+\dfrac{3}{14}>1\left(1\right)\)
Mặt khác:
\(\dfrac{3}{10}< \dfrac{3}{9}\\ \dfrac{3}{11}< \dfrac{3}{9}\\ \dfrac{3}{12}< \dfrac{3}{9}\\ \dfrac{3}{13}< \dfrac{3}{9}\\ \dfrac{3}{14}>\dfrac{3}{9}\)
\(\Rightarrow S=\dfrac{3}{10}+\dfrac{3}{11}+\dfrac{3}{12}+\dfrac{3}{13}+\dfrac{3}{14}< 5\cdot\dfrac{3}{9}\\ S=\dfrac{3}{10}+\dfrac{3}{11}+\dfrac{3}{12}+\dfrac{3}{13}+\dfrac{3}{14}< \dfrac{5}{3}< 2\left(2\right)\)
Từ (1) và (2) ta có: \(1< S< 2\)