Question

So sánh \(A=\dfrac{1}{4^2}+\dfrac{1}{5^2}+\dfrac{1}{6^2}+...+\dfrac{1}{21^2}\)và \(\dfrac{-3}{-8}\)

Answer 1

ta thấy:\(A=\dfrac{1}{4^2}+\dfrac{1}{5^2}+\dfrac{1}{6^2}+...+\dfrac{1}{21^2}< \dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{20.21}=\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{20}-\dfrac{1}{21}=\dfrac{1}{3}-\dfrac{1}{21}=\dfrac{2}{7}\)

=>A<\(\dfrac{2}{7}\)

lại thấy \(\dfrac{2}{7}=\dfrac{16}{56}\)(1)

\(\dfrac{-3}{-8}=\dfrac{3}{8}=\dfrac{21}{56}\left(2\right)\)

từ (1) và (2)

=>\(\dfrac{2}{7}< \dfrac{3}{8}\)

=>A<2/7<3/8 =>A<3/8