Question

CMR: 1/61+1/62+1/63+...+1/100>2/5

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Answer 1

ta có : \(\dfrac{1}{61}< \dfrac{1}{60}\\ \dfrac{1}{62}< \dfrac{1}{60}\\ ...\\ \dfrac{1}{100}< \dfrac{1}{60}\\ \Rightarrow\dfrac{1}{61}+\dfrac{1}{62}+\dfrac{1}{63}+...+\dfrac{1}{100}\left(c\text{ó}40.s\text{ố \dfrac{1}{60} }\right)\\ \Rightarrow\dfrac{1}{61}+\dfrac{1}{62}+\dfrac{1}{63}+...+\dfrac{1}{100}< \dfrac{40}{60}=\dfrac{2}{5}\)