chứng tỏ
1/2^2+1/3^2+1/2002^2+1/2003^2<1
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"đi khắp bầu trời : mẹ là tốt nhất ; ăn khắp trăm món : muối vẫn hàng đầu "
My name is Long and I’m a Vietnamese. I am twenty-four years old. I live in Ho Chi Minh city in the south of Vietnam.
I have a big family with six people. I have two sisters and a brother. My sisters are older and my brother is younger than me. My father is a teacher at a secondary school. He has worked for 35 years in the field and he is my biggest role model in life. My mother is a housewife. She is nice and she is really good at cooking. I love my family so much.
I’m a generous and easy-going person but when it comes to work I’m a competitive perfectionist. I’m also an optimis and outgoing person so I have many friends and other social relationships. I enjoy reading, writing and doing math. I decided to become a Civil Engineer because I have always been fascinated by bridges, buildings, and skyscrapers. A degree in Civil Engineering enables me to achieve my goals and also gives me an opportunity to make a difference in the community.
Five years from now, I want to become a project manager of a construction project. As a project manager, my primary goals are managing people, set budgets, and making decisions of all kinds. I also want to speak English fluently so I can work with people from different countries.
Put the words in the correct oder :
1 . from / vacation / come / Nha Trang / I / just / have / a / back / in .
->........... I just have come back from a vacation in Nha Trang.........................
2 . university / Viet Nam / the / was / Quoc Tu Giam / first / in
->...........The Quoc Tu Giam was the first university in VietNam.........
3 . world / sĩ / in / are / continents / there / the .
->...........There are six continents in the world...................
4 . England / tower / it / famous / in / the / is / most .
-> ............It is the famous tower in England...........................
5 . years / new / building / is / but / looks / 100 / more than / old / the it .
=> The old building is more than 100 years but it looks new
1 . from / vacation / come / Nha Trang / I / just / have / a / back / in .
=>I just have come back from a vacation in Nha Trang.
2 . university / Viet Nam / the / was / Quoc Tu Giam / first / in
->The Quoc Tu Giam was the first university in VietNam.
3 . world / sĩ / in / are / continents / there / the .
=>There are six continents in the world.
4 . England / tower / it / famous / in / the / is / most .
=>There are six continents in the world.
5 . years / new / building / is / but / looks / 100 / more than / old / the it .
=>The old building is more than 100 years but it looks new.
ta có 1/2^2<1/1.2;1/3^2<1/2.3;...;1/2002^2<2001.2002;1/2003^2<1/2002.2003
suy ra 1/1.2+1/2.3+...+1/2001.2002+1/2002.2003
= 1-2/2+1/2-1/3+...+1/2001-1/2002+1/2002-1/2003
=1-1/2003
mà 1/2^2+1/3^2+...+1/2002^2+1/2003^2<1-1/2003<1
Ta có:
1/22 = 1/1.2
1/32 < 1/2.3
1/20022 < 1/2001.2002
1/20032 < 1/2002.2003
Suy ra : 1/22 + 1/32 + 1/20022 + 1/20032 < 1/1.2 + 1/2.3 + 1/2001.2002 + 1/2002.2003
1/22 + 1/32 + 1/20022 + 1/20032 < (1 - 1/2 + 1/2 -1/3 )+(1/2001 - 1/2002 + 1/2002 -1/2003)
1/22 + 1/32 + 1/20022 + 1/20032 < 2/3 +1/2002 -1/2003<1
1/22 + 1/32 + 1/20022 + 1/20032 < 1