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Ta có: \(\frac{1}{2^2}< \frac{1}{1\cdot2};\frac{1}{3^2}< \frac{1}{2\cdot3};\frac{1}{4^2}< \frac{1}{3\cdot4};....;\frac{1}{100^2}< \frac{1}{99\cdot100}\)

\(\Rightarrow A< \frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{99\cdot100}\)

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

\(\Rightarrow A< 1-\frac{1}{100}< 1\left(đpcm\right)\)

Ta có : \(\frac{1}{2^2}=\frac{1}{4}< \frac{1}{1.2}\)

\(\frac{1}{3^2}=\frac{1}{9}< \frac{1}{2.3}\)

\(\frac{1}{4^2}=\frac{1}{16}< \frac{1}{3.4}\)

....

\(\frac{1}{100^2}=\frac{1}{10000}< \frac{1}{99.100}\)

Suy ra : \(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)

 \(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

\(=1-\frac{1}{100}=\frac{99}{100}< 1\)

Vậy ta có đpcm 

I love receiving gifts. Who doesn’t? Besides, exchanging gifts among ourselves is a great tradition in my part of the world whether there is an occasion for it or not. Anyway, I have been lucky to receive several gifts in my life, but today, I would to talk about a gift which I d a bit more than others. I received it at my last birthday.

The gift, I received, was a t-shirt – a polo t-shirt, when I was attending my university. Now, everybody in my family knew how much I actually to wear t-shirts. In fact, a perfect-looking t-shirt, made of cotton fabric, and blue jeans were my staple dress whether I was going to meet my boss in his office for a formal meeting or enjoying some football at a stadium with my friends.

However, even though, nobody really had anything against my t-shirt wearing habits, my youngest uncle didn’t really it that much. Of course, I could understand very well, why he didn’t me wearing a t-shirt 24/7, and it was because he thought that only juvenile persons would usually to wear a t-shirt and jeans. But, I was waiting for a big surprise on my 21st birthday when I found out that a beautiful looking, maroon colour t-shirt, made by the world-famous Polo company, was handed to me as a gift by none other than my youngest uncle! Besides, I felt my uncle actually had read my mind because, in fact, I had looked for such a beautiful t-shirt of that parular colour for a long time. To be honest, that gift was a “dream come true” to me!

Well, I d the gift so much because it has a perfect colour. Besides, it was made of 100 per cent, good quality, cotton fabric, so naturally, it was very comfortable to wear. Finally, the gift was so special to me because it was presented to me by a person who always had underestimated my preference in dress, especially, my preference for wearing a t-shirt.

Taylor Alison Swift (born December 13, 1989) is an American singer-songwriter, record producer, and actress. She is best known for her narrative songwriting that often centers around her personal life, which has received widespread crial praise and media coverage. At age 14, Swift became the youngest artist signed by the Sony/ATV Music publishing house and, at age 15, she signed her first record deal. Her 2006 eponymous debut studio album was the longest-charting album of the 2000s on the Billboard 200. Its third single, "Our Song", made her the youngest person to single-handedly write and perform a number-one song on the Billboard Hot Country Songs chart. Swift's breakthrough second studio album, Fearless (2008), won four Grammy Awards and produced the pop-crossover hit singles "Love Story" and "You Belong with Me". It became the best-selling album of 2009 in the United States and was certified Diamond by the RIAA.

Swift's self-written third studio album, Speak Now (2010), spawned the Grammy-winning single "Mean", and her genre-bending fourth studio album, Red (2012), earned Swift her first Billboard Hot 100 number-one single, "We Are Never Ever Getting Back Together". Her fifth studio album and first all-pop project, 1989 (2014), produced the number-one singles "Shake It Off" and "Blank Space" and won three Grammy Awards—including Album of the Year—making Swift the first woman to succeed herself at the top spot on the Hot 100 and the first woman to win Album of the Year twice as lead artist. Her hip hop-inspired sixth studio album, Reputation (2017), made her the first and only act in music history to have four albums each sell one million copies in their first week in the U.S. and generated her fifth Hot 100 number-one single, "Look What You Made Me Do". Her seventh studio album, Lover (2019), broke the record for the most simultaneous Hot 100 entries by a female artist and became the global best-selling studio album of 2019.

Having sold more than 50 million albums and 150 million singles globally, Swift is one of the world's best-selling music artists of all time. Her accolades include 10 Grammy Awards, an Emmy Award, and seven Guinness World Records; she is the most-awarded act and woman at the American Music Awards (29 wins) and Billboard Music Awards (23 wins), respectively. She has been included in multiple power rankings, such as Time's annual list of the 100 most influential people in the world (2010, 2015 and 2019), Rolling Stone's 100 Greatest Songwriters of All Time (2015), the Forbes Celebrity 100 (placing first in 2016 and 2019), and Billboard's Greatest of All Time Artists Chart (placing eighth). She was named Global Recording Artist of the Year twice by the IFPI (2014 and 2019), Woman of the Decade (2010s) by Billboard and the Artist of the Decade (2010s) by the American Music Awards.

Known as one of the most famous singer in the world, Taylor Swift is a typical example of an independent woman that inspires many young people including me. Taylor has achieved a number of awards and honors including :Grammy Awards,American Music Awards,Billboard Music Awards and so on.Her youtube channel has reached 31 million followers,and her best song : Shake it off has already had 2,6 billion views - a crazy number of which many singers always dream…. Her talent has shone through her incredible ability to write songs as well as a beautiful unique voice. Any lyrics in her songs have hidden messages which make a strong impression on listeners. Her songs are totally based on her life experiences – a distinctive style that sets her apart from other singers. Her charm and charisma is inevitable. Besides, she realized her special interest in music quite early and always has a supportive family when facing difficulties.In addition, her great influence on me goes beyond her musical talent. It is her character that is what I really admire about her. She won’t sit in the silence and avoid a problem if it causes defamation to her and not try to hide anything. She is also a strong supporter of feminism and has a range of famous and meaningful sayings that aspires us.Overall, Taylor Swift is a talented singer with admirable personalities and her life story would be a wonderful inspiration for those w ho are on their way to pursue their dreams.

yoz=50 độ .toy=130 độ.moy là góc vuông vì moy =90 độ

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