a) $U_{n+1}-U_{n} = \dfrac{2 - (n+1)}{\sqrt{n+1}}-\dfrac{2 - n}{\sqrt{n}}= \left ( \dfrac{2}{\sqrt{n+1}}-\sqrt{n+1}\right )- \left ( \dfrac{2}{\sqrt{n}}-\sqrt{n}\right )$$=2\left ( \dfrac{1}{\sqrt{n+1}}-\dfrac{1}{\sqrt{n}} \right )+\left ( \sqrt{n}-\sqrt{n+1}\right )do{1√n+1<1√n√n<√n+1\Rightarrow U_{n+1}-U_{n}<0\Rightarrow U_{n+1}<U_{n}$ Vậy dãy đã cho là dãy giảm.
a) Un+1−Un=2−(n+1)√n+1−2−n√n=2(1√n+1−1√n)+(√n−√n+1) do {1√n+1<1√n√n<√n+1⇒Un+1−Un<0⇒Un+1<Un Vậy dãy đã cho là dãy giảm.
a) $U_{n+1}-U_{n} = \dfrac{2 - (n+1)}{\sqrt{n+1}}-\dfrac{2 - n}{\sqrt{n}}=
\left ( \dfrac{2}{\sqrt{n+1}}-\sqrt{n+1}\right )- \left ( \dfrac{2}{\sqrt{n}}-\sqrt{n}\right )$$=2\left ( \dfrac{1}{\sqrt{n+1}}-\dfrac{1}{\sqrt{n}} \right )+\left ( \sqrt{n}-\sqrt{n+1}\right )
do{1√n+1<1√n√n<√n+1\Rightarrow U_{n+1}-U_{n}<0\Rightarrow U_{n+1}<U_{n}$ Vậy dãy đã cho là dãy giảm.