chứng minh

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

\(M=\frac{1}{1975}.\left(\frac{2}{1975}-1\right)-\frac{1}{1945}.\left(1-\frac{2}{1975}\right)-\frac{1974}{1975}.\frac{1946}{1945}-\frac{3}{1975.1945}\)

Tính giá trị biểu thức

\(M=\frac{1}{1975}.\left(\frac{2}{1975}-1\right)-\frac{1}{1945}.\left(1-\frac{2}{1975}\right)-\frac{1974}{1975}.\frac{1946}{1945}-\frac{3}{1975.1945}\)

Chứng tỏ rằng

\(\frac{1}{1945^2}\)\(+\frac{1}{1946^2}+\frac{1}{1947^2}+...+\frac{1}{1974^2}+\frac{1}{1975^2}\)<1/1944

Rút gọn biểu thức : \(B=\frac{1}{1975}\times\left(\frac{2}{1945}-1\right)-\frac{1}{1945}\times\left(1-\frac{2}{1975}\right)-\frac{1974}{1975}\times\frac{1946}{1945}-\frac{3}{1975\times1945}\)

Chứng minh:

\(\frac{1}{2^2}+\frac{1}{4^2}+\frac{1}{6^2}+\frac{1}{8^2}+...+\frac{1}{\left(2n\right)^2}< \frac{2016}{2017}\)

A=\(\frac{\frac{1}{2018}+\frac{2}{2017}+\frac{3}{2016}+....+\frac{2017}{2}+\frac{2018}{1}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....+\frac{1}{2019}}\). Chứng minh rằng A là số nguyên

Mong mọi người giúp

chứng minh rằng \(\frac{1}{5}+\frac{1}{13}+\frac{1}{25}+...+\frac{1}{2016^2+2017^2}<\frac{1}{2}\)

Rút gọn biểu thức 

\(B=\frac{1}{1975}.\left(\frac{2}{1945}-1\right)-\frac{1}{1945}.\left(1-\frac{2}{1975}\right)-\frac{1974}{1975}.\frac{1946}{1945}-\frac{3}{1975.1945}\)