Đáp án:
$Un=2^{n}+\frac{1}{n}$ là dãy tăng
limUn=lim($2^{n}+\frac{1}{n}$)=+∞
Giải thích các bước giải:
e)$Un=2^{n}+\frac{1}{n}$
Ta có:
$Un+1-Un=2^{n+1}+\frac{1}{n+1}-2^{n}-\frac{1}{n}$
<=>$Un+1-Un=2.2^{n}+\frac{1}{n+1}-2^{n}-\frac{1}{n}$
<=>$Un+1-Un=2^{n}+\frac{1}{n+1}-\frac{1}{n}$
<=>$Un+1-Un=2^{n}+\frac{n-(n+1)}{n.(n+1)}$
<=>$Un+1-Un=2^{n}+\frac{-1}{n.(n+1)}>0$
•limUn=lim($2^{n}+\frac{1}{n}$)=+∞
