\(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+......+\frac{1}{99}+\frac{1}{100}\)
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Những câu hỏi liên quan
NH
2
18 tháng 3 2017
Ta có :
\(\frac{1}{10}>\frac{1}{20}\)
\(\frac{1}{11}>\frac{1}{20}\)
\(\frac{1}{12}>\frac{1}{20}\) \(\Rightarrow\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+.....+\frac{1}{19}>\frac{1}{20}+\frac{1}{20}+....+\frac{1}{20}=\frac{10}{20}=\frac{1}{2}\)(1)
.....
\(\frac{1}{19}>\frac{1}{20}\)
Ta có :
\(\frac{1}{20}>\frac{1}{30}\)
\(\frac{1}{21}>\frac{1}{30}\)
\(\frac{1}{22}>\frac{1}{30}\) \(\Rightarrow\frac{1}{20}+\frac{1}{21}+\frac{1}{22}+....+\frac{1}{29}>\frac{1}{30}+\frac{1}{30}+....+\frac{1}{30}=\frac{10}{30}=\frac{1}{3}\)(2)
........
\(\frac{1}{29}>\frac{1}{30}\)
Ta có :
\(\frac{1}{30}>\frac{1}{40}\)
\(\frac{1}{31}>\frac{1}{40}\) \(\Rightarrow\frac{1}{30}+\frac{1}{31}+....+\frac{1}{39}>\frac{1}{40}+\frac{1}{40}+.....+\frac{1}{40}=\frac{10}{40}=\frac{1}{4}\)(3)
.........
\(\frac{1}{39}>\frac{1}{40}\)
Từ 1 , 2 , 3 ,
=> \(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+.....+\frac{1}{39}>\frac{1}{2}+\frac{1}{3}+\frac{1}{4}=\frac{13}{12}>1\)
=> ....... > 1
DR
0
21 tháng 2 2017
Ta có:
\(\frac{1}{10}+\frac{1}{11}+...+\frac{1}{49}>\frac{1}{50}+\frac{1}{50}+...+\frac{1}{50}=\frac{40}{50}=\frac{4}{5}\)
\(\frac{1}{50}+\frac{1}{51}+...+\frac{1}{99}>\frac{1}{100}+\frac{1}{100}+...+\frac{1}{100}=\frac{50}{100}=\frac{1}{2}\)
Từ đây ta suy ra
A > \(\frac{4}{5}+\frac{1}{2}+\frac{1}{100}=1,31>1\)
YP
1
DP
28 tháng 2 2017
30 số hạng đầu lớn hơn 1
\(\frac{1}{10}+\frac{1}{11}+..+\frac{1}{19}>\frac{1}{20}+\frac{1}{20}+..+\frac{1}{20}=\frac{1}{2}\)\(\frac{1}{2}\)
\(\frac{1}{20}+\frac{1}{21}+..+\frac{1}{29}>\frac{1}{30}+\frac{1}{30}+..+\frac{1}{30}=\frac{1}{3}\)
\(\frac{1}{30}+\frac{1}{31}+...+\frac{1}{39}>\frac{1}{40}+\frac{1}{40}+...+\frac{1}{40}=\frac{1}{4}\)
=> \(\frac{1}{10}+\frac{1}{11}+...+\frac{1}{39}>\frac{1}{2}+\frac{1}{3}+\frac{1}{4}=\frac{13}{12}>1\)
LT
3
7 tháng 4 2019
\(A=\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+...+\frac{1}{99}+\frac{1}{100}\)
\(A=\frac{1}{10}+\left(\frac{1}{11}+\frac{1}{12}+...+\frac{1}{99}+\frac{1}{100}\right)>\frac{1}{10}+\left(\frac{1}{100}+\frac{1}{100}+...+\frac{1}{100}\right)\)
\(A=\frac{1}{10}+\frac{99}{100}=1\)
=> A > 1
B
7 tháng 4 2019
\(A=\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+...+\frac{1}{99}+\frac{1}{100}\)
\(A=\frac{1}{10}+\frac{1}{11}+...+\frac{1}{19}>\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}=\frac{10}{20}=\frac{1}{2}\)
\(A=\frac{1}{20}+\frac{1}{21}+...+\frac{1}{29}>\frac{1}{30}+\frac{1}{30}+...+\frac{1}{30}=\frac{10}{30}=\frac{1}{3}\)
\(A=\frac{1}{30}+\frac{1}{31}+...+\frac{1}{39}>\frac{1}{40}+\frac{1}{40}+... +\frac{1}{40}=\frac{10}{40}=\frac{1}{4}\)
\(\Rightarrow A>1\)
DL
22 tháng 6 2017
\(A=\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+...+\frac{1}{100}\)
\(=\frac{1}{10}+\left(\frac{1}{11}+\frac{1}{12}+...+\frac{1}{99}+\frac{1}{100}\right)>\frac{1}{10}+\left(\frac{1}{100}+\frac{1}{100}+...+\frac{1}{100}\right)\)
\(=\frac{1}{10}+\frac{90}{100}>1\)
\(A>1\left(đpcm\right)\)