chứng minh: $\frac{1}{(n+1)\sqrt{n}+n\sqrt{n+1}}$ = $\frac{1}{\sqrt{n}}$ – $\frac{1}{\sqrt{n+1}}$
chứng minh: $\frac{1}{(n+1)\sqrt{n}+n\sqrt{n+1}}$ = $\frac{1}{\sqrt{n}}$ – $\frac{1}{\sqrt{n+1}}$
By Cora
By Cora
chứng minh: $\frac{1}{(n+1)\sqrt{n}+n\sqrt{n+1}}$ = $\frac{1}{\sqrt{n}}$ – $\frac{1}{\sqrt{n+1}}$
Giải thích các bước giải:
$\dfrac{1}{\sqrt{n}} – \dfrac{1}{\sqrt{n + 1}} = \dfrac{\sqrt{n + 1} – \sqrt{n}}{\sqrt{n\left ( n + 1 \right )}} = \dfrac{\left ( \sqrt{n + 1} – \sqrt{n} \right )\left ( \sqrt{n + 1} + \sqrt{n} \right )}{\sqrt{n\left ( n + 1 \right )}\left ( \sqrt{n + 1} + \sqrt{n} \right )} = \dfrac{n + 1 – n}{\left ( n + 1 \right )\sqrt{n} + n\sqrt{n + 1}} = \dfrac{1}{\left ( n + 1 \right )\sqrt{n} + n\sqrt{n + 1}}$