Question

bài 5 thôi

cảm ơn nhìu nha!!!!

Answer 1

Bài 5:

\(\dfrac{1}{2^2}< \dfrac{1}{1.2};\dfrac{1}{3^2}< \dfrac{1}{2.3};...;\dfrac{1}{2019^2}< \dfrac{1}{2018.2019}\)

\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{2019^2}< \dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{2018.2019}\)

\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{2019^2}< 1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{2018}-\dfrac{1}{2019}\)

\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{2019^2}< 1-\dfrac{1}{2019}\)

\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{2019^2}< \dfrac{2018}{2019}< 1\left(đpcm\right)\)