Bài 1: Căn bậc hai
Các câu hỏi tương tự
CMR n\(\in\)N, n>3
a,\(\frac{1}{2\sqrt{1} }+\frac{1}{3\sqrt{2} } +\frac{1}{4\sqrt{3} }+...+\frac{1}{(n+1)\sqrt{n} }<2 \)
b,S=\(\frac{1}{3(1+\sqrt{2}) }+\frac{1}{5(\sqrt{2}+\sqrt{3} }+...+\frac{1}{(2n+1)(\sqrt{n}+\sqrt{n+1}) } \)
CMR n\(\in \)N
\(1\le \frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2} +...+\frac{1}{n^2} \le \frac{5}{3} \)
@Akai Haruma giúp mình
1.Chứng minh: \(\frac{1}{2\cdot\sqrt{1}}+\frac{1}{3\cdot\sqrt{2}}+\frac{1}{4\cdot\sqrt{3}}+...+\frac{1}{2012\cdot\sqrt{2011}}+\frac{1}{2013\cdot\sqrt{2012}}\)\(< 2\)
2.Chứng minh: A= \(\frac{1}{3\cdot\left(\sqrt{1}+\sqrt{2}\right)}+\frac{1}{5\cdot\left(\sqrt{2}+\sqrt{3}\right)}+...+\frac{1}{97\cdot\left(\sqrt{48}+\sqrt{49}\right)}\)\(< \frac{1}{2}\)
CMR n\(\in \)N, n>3
\(\frac{1}{1^3}+\frac{1}{2^3}+\frac{1}{3^3}+...+\frac{1}{n^3} <2 \)
Cho n là số tự nhiên khác 0. Tìm giá trị nhỏ nhất của
Q= \(\sqrt{1+\frac{1}{1^2}+\frac{1}{2^2}}+\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+\sqrt{1+\frac{1}{3^2}+\frac{1}{4^2}}+....+\sqrt{1+\frac{1}{n^2}+\frac{1}{\left(n+1\right)^2}}+\frac{101}{n+1}\)
CMR
\(\sqrt{\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{\left(a+b\right)^2}}=\left|\frac{1}{a}+\frac{1}{b}-\frac{1}{a+b}\right|\)
Cho a+b+c=0
CMR : \(\sqrt{\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}}\) =/\(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\)/
Cho a,b,c >0 tm abc=1 CMR
\(\frac{1}{(a+1)^2+b^2+1}+\frac{1}{(b+1)^2+c^2+1}\frac{1}{(c+1)^2+a^2+1} \le\frac{1}{2} \)
\(\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+...+\frac{1}{\sqrt{48}}\)