\(\frac{1}{1975^2}+\frac{1}{1976^2}+...+\frac{1}{2017^2}< \frac{1}{1974.1975}+\frac{1}{1975.1976}+...+\frac{1}{2016.2017}\)
\(=\frac{1}{1974}-\frac{1}{1975}+\frac{1}{1975}-\frac{1}{1976}+...+\frac{1}{2016}-\frac{1}{2017}=\frac{1}{1974}-\frac{1}{2017}< \frac{1}{1974}\)
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
Chứng minh:
\(\frac{1}{2^2}+\frac{1}{4^2}+\frac{1}{6^2}+\frac{1}{8^2}+...+\frac{1}{\left(2n\right)^2}< \frac{2016}{2017}\)
Câu 1: Tính
B=\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{97.98.99}+\frac{1}{98.99.100}\)
Câu 2: CMR:
A=75.(41975+41974+....+42+5)+25 chia hết cho 41976
\(\left(\frac{1}{2}+\frac{2015}{2016}+\frac{2016}{2017}+1\right)\left(\frac{2105}{2016}+\frac{2016}{2017}+\frac{7}{22}\right)-\left(\frac{1}{2}+\frac{2015}{2016}+\frac{2016}{2017}\right)\left(\frac{2015}{2016}+\frac{2016}{2017}+\frac{7}{22}+1\right)\)
chứng tỏ \(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{2016}}+\frac{1}{2^{2017}}< 1\)
\(A=\frac{1}{2017}+\frac{2}{2017^2}+\frac{3}{2017^3}+...+\frac{2017}{2017^{2017}}+\frac{2018}{2017^{2018}}\). Chứng minh rằng : A < \(\frac{2017}{2016^2}\)
SO SÁNH:
A=\(\frac{\frac{2016}{1}+\frac{2015}{2}+\frac{2014}{3}+.....+\frac{2}{2015}+\frac{1}{2016}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+.....+\frac{1}{2016}+\frac{1}{2017}}\)
VÀ
B=2017
\(A=\frac{\frac{2017}{1}+\frac{2016}{2}+\frac{2015}{3}+...+\frac{1}{2017}+2017}{1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2017}}\)
A = \(\frac{2017}{2016^2+1}+\frac{2017}{2016^2+2}+...+\)\(\frac{2017}{2016^2+2016}\)
Chứng minh A không phải là số nguyên dương
