<p>Show that&nbsp;$\frac{1}{\sqrt{a}-\sqrt{a+1}}=-\left( \sqrt{a}+\sqrt{a+1} \right)$ and thus evaluate $\frac{1}{1-\sqrt{2}}-\frac{1}{\sqrt{2}-\sqrt{3}}+\frac{1}{\sqrt{3}-\sqrt{4}}-...+\frac{{{\left( -1 \right)}^{k+1}}}{\sqrt{k}-\sqrt{k+1}}$ , where&nbsp;$k$ is even.</p>

Show that $\frac{1}{\sqrt{a}-\sqrt{a+1}}=-\left( \sqrt{a}+\sqrt{a+1} \right)$ and thus evaluate $\frac{1}{1-\sqrt{2}}-\frac{1}{\sqrt{2}-\sqrt{3}}+\frac{1}{\sqrt{3}-\sqrt{4}}-...+\frac{{{\left( -1 \right)}^{k+1}}}{\sqrt{k}-\sqrt{k+1}}$ , where $k$ is even.

Surds - Higher Order Thinking Questions

Question b2b4c16a

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