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Nguyễn Thị Lệ Hoa
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soyeon_Tiểubàng giải
21 tháng 10 2016 lúc 12:55

\(M=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{62}+\frac{1}{63}\)

\(M=1+\left(\frac{1}{2}+\frac{1}{3}\right)+\left(\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}\right)+\left(\frac{1}{8}+\frac{1}{9}+...+\frac{1}{15}\right)+\left(\frac{1}{16}+\frac{1}{17}+...+\frac{1}{31}\right)+\left(\frac{1}{32}+\frac{1}{33}+...+\frac{1}{63}\right)\)

\(M< 1+\frac{1}{2}.2+\frac{1}{4}.4+\frac{1}{8}.8+\frac{1}{16}.16+\frac{1}{32}.32\)

\(M< 1+1+1+1+1+1\)

\(M< 1.6=6\left(đpcm\right)\)

Lê Đức Anh
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Lê Đức Anh
20 tháng 7 2016 lúc 19:10

Ta có: A = 1/2+1/3+1/4+...+1/62+1/63+1/64

A = 1+(1/2+1/3+1/4)+(1/5+1/6+1/7+1/8)+(1/9+1/10+...+1/16)+...+(1/17+1/18+....+1/32)+(1/33+1/34+...+1/64)

Ta có: 1/2+1/3+1/4>1/2+1/4+1/4=1

1/5+1/6+1/7+1/8>1/8+1/8+1/8+1/8=1/8.4=1/2

1/9 +1/10+...+1/16>1/16+1/16+...1/16=1/16.8=1/2

1/33+1/34+...+1/64>1/64+1/64+...+1/64=1/64.32=1/2

Vậy A > 4

Lê Đức Anh
17 tháng 7 2016 lúc 19:56

Xin ai giải hộ cái

nguyen hong phuc
6 tháng 7 2017 lúc 9:36

Ta có A = 1 + 1/2 + 1/3 + 1/4 + 1/5 + ... + 1/64

          A = 1 + (1/2 + 1/3 + 1/4) + (1/5 + 1/6 + ... + 1/8) + (1/9 + 1/10 + 1/11 + ... + 1/16) + (1/17 + 1/18 + 1/19 + ... + 1/32) + (1/33 + 1/34 + 1/35 + ... + 1/64)

=> A > 1 +  (1/2 + 1/4.2) + 1/8.4 + 1/16.8 + 1/32.16 + 1/64.32

     A > 1 + 1 + 1/2 + 1/2 + 1/2 + 1/2

    A > 4 (DPCM).

Nguyễn Lâm Hùng
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Uzumaki Naruto
12 tháng 8 2016 lúc 9:24

Ta có: \(\frac{1}{3^2}< \frac{1}{2.3};\frac{1}{4^2}< \frac{1}{3.4};\frac{1}{5^2}< \frac{1}{4.5};....;\frac{1}{100^2}< \frac{1}{99.100}\)

\(\Rightarrow\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+...+\frac{1}{100^2}< \frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\)

\(\Rightarrow\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+...+\frac{1}{100^2}< \frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)

\(\Rightarrow\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+...+\frac{1}{100^2}< \frac{1}{2}-\frac{1}{100}\)

\(\Rightarrow\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+...+\frac{1}{100^2}< \frac{49}{100}< \frac{1}{2}\)

Vậy \(C=\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+...+\frac{1}{100^2}< \frac{1}{2}\)

Nguyễn Lâm Hùng
12 tháng 8 2016 lúc 9:26

Ko hỉu

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luuly
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Phương
22 tháng 10 2018 lúc 12:45

My mother is the one who I love most in my life. For what she’s done, she deserved with the whole world. My mother is a 43-year-old household wife. She’s tall, slim and especially she has a beautiful long black hair. She always smile thus everyone consider her a friendly person. My mom loves every members of the family with all her heart. She agreed to be a household woman instead of working out. My mother takes care of the household chorces. She wakes up earliest in the morning and goes to bed latest in the night. And during the day, she’s very busy. I remember once when my mother got sick so nobody did the house work and everything went to crazy. From then, my father and I join hand to help mother whenever we have free time. She’s really happy about that. When I was a kid, mom taught me to play piano at each weekend. I still remember the songs which includes many childhood’s experiences. Not only taught me to play piano, she also taught me to be a better human. I love the moral stories that she told me before I fell asleep every night. We’re really appreaciate mother’s effort, patient and her hard work to conserve the family’s happiness. My mother is an indispensable part of my life. When I grow up, I want to be a woman her.

Nguyễn Mai Hương
22 tháng 10 2018 lúc 14:05

The one I love and respect most is my mother. My mother is 48 years old. She is tall and rather thin. She is a warm kindly person with an oval face and a long-silky hair. She is a farmer. She has to work hard to support (can use “feed”) us. She is very strict. Thanks to that I am educated into a good person and teached  many things in  life. My mother loves cooking and cooks very well. I to eat whatever she cooks. In my freetime, I always do the house works with her that make her very happy. My mother loves us so much. She said we were the happiest things in her life. The love she gave us s sky. It’s very great. Sometimes, there are many difficulties which make me down. But when I know that she is always waiting me, I feel warm and peace.  My mother becomes my pride in whatever I do and wherever I go. I will try my best to relive suffering among her life and give her a more comfortale and happy life. I love my mother so much

Phương
22 tháng 10 2018 lúc 12:46

The one i love most is my mother. She is tall and rather thin
She is a warm kindly person with an oval face and a long-silky hair.
My mother loves us very much. She is used to staying up late and getting up early to earn money and take care of us. She is strict thanks to that we are educated into a good person.I will try to study well to satisfy my mother's faith.

nguyen hoa
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nguyen hoa
4 tháng 3 2016 lúc 18:47

các bạn giúp mình nhé, người làm nhanh và đúng sẽ được mình k nhé

Nguyệt Nguyễn
7 tháng 4 lúc 19:26

Ta có: A = 1/2+1/3+1/4+...+1/62+1/63+1/64

A = 1+(1/2+1/3+1/4)+(1/5+1/6+1/7+1/8)+(1/9+1/10+...+1/16)+...+(1/17+1/18+....+1/32)+(1/33+1/34+...+1/64)

Ta có: 1/2+1/3+1/4>1/2+1/4+1/4=1

1/5+1/6+1/7+1/8>1/8+1/8+1/8+1/8=1/8.4=1/2

1/9 +1/10+...+1/16>1/16+1/16+...1/16=1/16.8=1/2

1/33+1/34+...+1/64>1/64+1/64+...+1/64=1/64.32=1/2

Vậy A > 4

Kudo shinichi
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nghiem thi huyen trang
17 tháng 4 2017 lúc 19:30

ta thấy:

A<\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+.....+\frac{1}{100.101}=\frac{1}{2}-\frac{1}{101}=\frac{99}{202}< 1\)

mà 1<2

=>A<2

vậy.......................

Ngọc Lan
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Mạnh Hùng Phan
13 tháng 4 2019 lúc 16:04

A=1+(1/2 + 1/3 + 1/4)+(1/5 + 1/6 + 1/7 + 1/8)+(1/9+...+1/16)+(1/17+...+1/32)+(1/33+...+1/64)

A>1+(1/2 + 1/4 + 1/4)+(1/8+ 1/8+ 1/8+ 1/8)+(1/16+1/16+...+1/16)+(1/64+...+1/64)

A>1 + 1 + 1/2 + 1/2 + 1/2+ 1/2

A>4

Lê Quỳnh Trang
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Ngo Tung Lam
20 tháng 4 2018 lúc 21:35

Ta có :

\(S=\frac{1}{17}+\frac{1}{18}+\frac{1}{19}+.......+\frac{1}{62}+\frac{1}{63}+\frac{1}{64}\)

\(\Rightarrow S< \frac{1}{17}+\frac{1}{17}+......+\frac{1}{17}+\frac{1}{17}+\frac{1}{17}\)

\(\Rightarrow S< \frac{1}{17}.48\)

\(\Rightarrow S< \frac{48}{17}\)

\(\Rightarrow S< 2\)( 1 ) 

Lại có :

\(S>\frac{1}{64}+\frac{1}{64}+.........+\frac{1}{64}+\frac{1}{64}+\frac{1}{64}\)

\(\Rightarrow S>\frac{1}{64}.48\)

\(\Rightarrow S>\frac{3}{4}\)( 2 ) 

Từ ( 1 ) và ( 2 ) suy ra : \(\frac{3}{4}< S< 2\)

Vậy \(1< S< 2\left(ĐPCM\right)\)