\(A=\frac{3}{1^2x2^2}+\frac{5}{2^2x3^2}+\frac{7}{3^2x4^2}+............+\frac{19}{9^2x10^2}\)
\(A=\frac{3}{1^2x2^2}+\frac{5}{2^2x3^2}+\frac{7}{3^2x4^2}+......+\frac{39}{19^2x20^2}\)
Tính A
Chứng minh rằng: \(\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+.....+\frac{2013}{2006^2.2007^2}<1\)
Chứng minh: \(\frac{1}{2}+\frac{2}{2^2}+\frac{3}{2^3}+..+\frac{n}{2^n}+...+\frac{2013}{2^{2013}}+\frac{2014}{2^{2014}}<2\)
Chứng minh:\(S=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+........+\frac{1}{2014^2}< \frac{2013}{2014}\)
cho đa thức f(x)=\(x\left(\frac{x^{2013}}{3}-\frac{x^{2014}}{5}+\frac{x^{2015}}{7}+\frac{x^2}{2}\right)-\)\(\left(\frac{x^{2014}}{3}-\frac{x^{2015}}{5}+\frac{x^{2016}}{7}+\frac{x^2}{2}\right)\).chứng minh đa thức f(x) nhận giá trị nguyên với mọi giá trị x nguyên
Chứng minh rằng : \(\frac{1}{4028}< \left(\frac{1}{2}.\frac{3}{4}.....\frac{2011}{2012}.\frac{2013}{2014}\right)^2< \frac{1}{2015}\)
\(A=\frac{1}{2}+\left(\frac{1}{2}\right)^2\left(\frac{1}{2}\right)^3+...+\left(\frac{1}{2}\right)^{2013}+\left(\frac{1}{2}\right)^{2014}\)
Chứng minh A< 1
chứng minh \(\frac{1}{3^2}+\frac{1}{5^2}+\frac{1}{7^2}+.....+\frac{1}{2019^2}< \frac{1}{12}\)