Với \(n=1\) thì đề sai, mà hình như với số nào đề cũng sai...
Các câu hỏi tương tự
CMR: \(\forall n\in N\)thì \(\left|\left\{\frac{n}{1}\right\}-\left\{\frac{n}{2}\right\}+\left\{\frac{n}{3}\right\}-...-\left(-1\right)^n\left\{\frac{n}{n}\right\}\right|< \sqrt{2n}\)
\(n\ge3;n\inℕ\)
CMR:
\(\frac{1}{a^n\left(b+c\right)}+\frac{1}{b^n\left(c+a\right)}+\frac{1}{c^n\left(a+b\right)}\ge\frac{3}{2}\)
CMR
\(\left(1+\frac{1}{m}\right)^m< \left(1+\frac{1}{n}\right)^n< \left(1-\frac{1}{n}\right)^{-n}< \left(1-\frac{1}{m}\right)^{-m}\)
\(\forall\:1\le m< n\:\in N\)
CMR:
\(\left(n+1\right)\left(n+2\right)...\left(n+n\right)⋮2^n\left(\forall n\in N\cdot\right)\)
Cho \(n\inℕ^∗\)CMR
\(\sqrt{1+\frac{1}{n^2}+\frac{1}{\left(n+1\right)^2}}=1+\frac{1}{n}-\frac{1}{\left(n+1\right)}\)
Cho \(n\inℕ^∗\) CMR
\(\sqrt{1+\frac{1}{n^2}+\frac{1}{\left(n+1\right)^2}}=1+\frac{1}{n}-\frac{1}{\left(n+1\right)}\)
Bài 1: Cho \(x_n=-\frac{2655}{2}.\left(-1\right)^n+\frac{1349}{10}.5^n-1995\)
CMR: \(x_{2016}⋮2017\)
Bài 2: Cm: \(2^{n-1}\left(x^n+y^n\right)\ge\left(x+y\right)^n,\forall n\in N^{\cdot}\)
CMR: \(\left(2+\frac{a}{b}\right)^{\alpha}+\left(2+\frac{b}{c}\right)^{\alpha}+\left(2+\frac{c}{a}\right)^{\alpha}\ge3^{\alpha+1}\left(\forall a,b,c>0\right)\)
CMR
\(\left(2a+\frac{1}{b}+\frac{1}{c}\right)\left(2b+\frac{1}{c}+\frac{1}{a}\right)\left(2c+\frac{1}{a}+\frac{1}{b}\right)\ge64\left(\forall a,b,c>0\right)\)