Ta có: \(\frac{1}{1^2}=\frac{1}{1\cdot1};\frac{1}{2^2}<\frac{1}{1\cdot2};...;\frac{1}{50^2}<\frac{1}{49\cdot50}\)
=>\(\frac{1}{1^2}+\frac{1}{2^2}+...+\frac{1}{50^2}<1+\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{49\cdot50}=1+1-\frac{1}{50}=2-\frac{1}{50}=1,98\)
hay A<1,98 mà 1,98<2 nên A<2
Vậy A<2
A=\(\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+.........+\frac{1}{50^{^2}}\) chứng minh A > 2
cho abc=1 , chứng minh :
\(\frac{1}{a^2+2b^2+3}+\frac{1}{b^2+2c^2+3}+\frac{1}{c^2+2a^2+3}\le\frac{1}{2}\)
Cho biểu thức A = \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{100}}\)
Chứng tỏ 0 < A < 1
Cho A=\(\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{50^2}\)
Cho \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=2\) và a+b+c=abc. Chứng minh rằng: \(\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}=2\)
Cho A = \(\frac{1}{2}.\frac{3}{4}\frac{5}{6}...\frac{2011}{2012}\). Chứng minh: A2 < \(\frac{1}{2013}\).
Chứng minh rằng \(M=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{n^2}
Chứng minh rằng: \(\frac{1}{4^2}+\frac{1}{6^2}+\frac{1}{8^2}+...+\frac{1}{\left(2n\right)^2}
