\(\dfrac{1}{12}>\dfrac{1}{22};\dfrac{1}{13}>\dfrac{1}{22};...;\dfrac{1}{21}>\dfrac{1}{22};\dfrac{1}{22}=\dfrac{1}{22}\)
\(\Rightarrow\dfrac{1}{12}+\dfrac{1}{13}+\dfrac{1}{14}+...+\dfrac{1}{22}>\dfrac{1}{22}.11\) (do A có 11 số hạng)
\(\Leftrightarrow A>\dfrac{11}{22}=\dfrac{1}{2}\) ( đpcm)
cho tổng B=\(\dfrac{1}{12}+\dfrac{1}{13}+\dfrac{1}{14}+...+\dfrac{1}{22}\). Chứng minh rằng: B > \(\dfrac{1}{2}\)
Bài 1:
a, Cho A = \(\dfrac{1}{2^2}+\dfrac{1}{4^2}+\dfrac{1}{6^2}+....+\dfrac{1}{100^2}\)
Chứng tỏ: A <\(\dfrac{1}{2}\)
b, Cho B = \(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+....+\dfrac{1}{2^{20}}\)
Chứng tỏ B < 1
c, Cho C = \(\dfrac{1}{5}+\dfrac{1}{13}+\dfrac{1}{14}+\dfrac{1}{15}+\dfrac{1}{61}+\dfrac{1}{62}+\dfrac{1}{63}\)
Chứng tỏ C < \(\dfrac{1}{2}\)
d, Cho D = \(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{20^2}\)
Chứng tỏ D < 1
Bài 1: Chứng tỏ rằng :
\(\dfrac{11}{15}< \dfrac{1}{21}+\dfrac{1}{22}+......+\dfrac{1}{60}< \dfrac{3}{2}\)
Bài 2: Chứng tỏ rằng:
\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+......+\dfrac{1}{n^2}< 1\)
\(\dfrac{1}{4}+\dfrac{1}{16}+\dfrac{1}{36}+\dfrac{1}{100}+\dfrac{1}{144}+\dfrac{1}{196}< \dfrac{1}{2}\)
\(\dfrac{1}{5}+\dfrac{1}{13}+\dfrac{1}{25}+\dfrac{1}{41}+\dfrac{1}{61}+\dfrac{1}{85}+\dfrac{1}{113}< \dfrac{1}{2}\)
Cho S = \(\dfrac{1}{11}+\dfrac{1}{12}+\dfrac{1}{13}+\dfrac{1}{14}+\dfrac{1}{15}+\dfrac{1}{16}+\dfrac{1}{17}+\dfrac{1}{18}+\dfrac{1}{19}+\dfrac{1}{20}\). Hãy so sánh S và \(\dfrac{1}{2}\)
1.Tính nhanh
A=\(\dfrac{2}{7}\)+\(\dfrac{-3}{8}\)+\(\dfrac{11}{7}\)+\(\dfrac{1}{3}\)+\(\dfrac{1}{7}\)+\(\dfrac{5}{-3}\)
B=\(\dfrac{3}{17}\)+\(\dfrac{-5}{13}\)+\(\dfrac{-18}{35}\)+\(\dfrac{14}{17}\)+\(\dfrac{17}{-35}\)+\(\dfrac{-8}{13}\)
C=\(\dfrac{-3}{17}\)+(\(\dfrac{2}{3}\)+\(\dfrac{3}{17}\))
D=(\(\dfrac{-1}{6}\)+\(\dfrac{5}{-12}\))+\(\dfrac{7}{12}\)
2.a) Chứng tỏ:\(\dfrac{1}{201}\)+\(\dfrac{1}{212}\)+. . .+\(\dfrac{1}{399}\)+\(\dfrac{1}{400}\)
b)1 < \(\dfrac{1}{5}\)+\(\dfrac{1}{6}\)+. . .+\(\dfrac{1}{16}\)+\(\dfrac{1}{17}\)< 2
tính một cách hợp lí:
A) \(4\dfrac{3}{4}+\left(-0,37\right)+\dfrac{1}{8}+\left(-1,28\right)+\left(-2,5\right)+3\dfrac{1}{12}\)
b) \(\dfrac{3}{5.7}+\dfrac{3}{7.9}+...+\dfrac{3}{59.61}\)
c) \(\dfrac{\dfrac{5}{22}+\dfrac{3}{13}-\dfrac{1}{2}}{\dfrac{4}{13}-\dfrac{2}{11}+\dfrac{3}{2}}\)
Tính:
a. \(\dfrac{-5}{14}-\dfrac{2}{14}+\dfrac{1}{8}+\dfrac{1}{8}\)
b.\(\dfrac{-5}{22}-1+\dfrac{3}{2}-\dfrac{6}{22}\)
c.\(\dfrac{2}{5}+\dfrac{5}{4}+(\dfrac{-2}{5}+\dfrac{5}{4})-\dfrac{5}{2}\)
d.\(\dfrac{-1}{2}+\dfrac{1}{4}+\dfrac{2}{8}-\dfrac{11}{77}\)
làm nhanh hộ mình nha!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Chứng minh rằng: \(\dfrac{1}{11}+\dfrac{1}{12}+\dfrac{1}{13}+....+\dfrac{1}{70}>\dfrac{4}{3}\)
Cho S =\(\dfrac{1}{11}+\dfrac{1}{12}+\dfrac{1}{13}+\dfrac{1}{14}+\dfrac{1}{15}+\dfrac{1}{16}+\dfrac{1}{17}+\dfrac{1}{18}+\dfrac{1}{19}+\dfrac{1}{20}\)
Hãy so sánh S và \(\dfrac{1}{2}\)
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