Question

chứng minh

\(\dfrac{1}{1975^2}+\dfrac{1}{1976^2}+\dfrac{1}{1977^2}+...+\dfrac{1}{2016^2}+\dfrac{1}{2017^2}< \dfrac{1}{1974}\)

Answer 1

Ta có : \(\dfrac{1}{1794}\)>\(\dfrac{1}{1795^2}\)

\(\dfrac{1}{1794}\)>\(\dfrac{1}{1796^2}\)

\(\dfrac{1}{1794}\)>\(\dfrac{1}{1797^2}\)

.....................

\(\dfrac{1}{1794}\)>\(\dfrac{1}{2016^2}\)

\(\dfrac{1}{1794}\)>\(\dfrac{1}{2017^2}\)

\(\Leftrightarrow\)\(\dfrac{1}{1794}\)>\(\dfrac{1}{1795^2}\)+\(\dfrac{1}{1796^2}\)+\(\dfrac{1}{1797^2}\)+. . .+\(\dfrac{1}{2016^2}\)+\(\dfrac{1}{2017^2}\)

Answer 2

Chúc bạn học tốt

Answer 3