Are you thinking about rationalizing the denominator?

Algebra Level 3

\[ \large \dfrac{1}{2\sqrt1+1\sqrt2}+\dfrac{1}{3\sqrt2+2\sqrt3}+\dfrac{1}{4\sqrt3+3\sqrt4}+\dots+\dfrac{1}{25\sqrt{24}+24\sqrt{25}} =\, ? \]

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