[tex]\it \dfrac{\sqrt k-\sqrt{k-1}}{\sqrt{ k(k-1)}}=\dfrac{1}{\sqrt{k-1}}-\dfrac{1}{\sqrt k}\\ \\ \\ Expresia\ din\ enun\c{\it t}\ devine\ :\\ \\ \\ 1-\dfrac{1}{\sqrt2}+\dfrac{1}{\sqrt2}-\dfrac{1}{\sqrt3}+\dfrac{1}{\sqrt3}-\dfrac{1}{\sqrt4}+\ ...\ +\dfrac{1}{\sqrt{63}}-\dfrac{1}{\sqrt{64}}=1-\dfrac{1}{\sqrt{64}}=1-\dfrac{1}{8}}=\dfrac{7}{8}[/tex]
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[tex]\it \dfrac{\sqrt k-\sqrt{k-1}}{\sqrt{ k(k-1)}}=\dfrac{1}{\sqrt{k-1}}-\dfrac{1}{\sqrt k}\\ \\ \\ Expresia\ din\ enun\c{\it t}\ devine\ :\\ \\ \\ 1-\dfrac{1}{\sqrt2}+\dfrac{1}{\sqrt2}-\dfrac{1}{\sqrt3}+\dfrac{1}{\sqrt3}-\dfrac{1}{\sqrt4}+\ ...\ +\dfrac{1}{\sqrt{63}}-\dfrac{1}{\sqrt{64}}=1-\dfrac{1}{\sqrt{64}}=1-\dfrac{1}{8}}=\dfrac{7}{8}[/tex]