=>
We rationalize the denominator of each fraction to give
\(\frac{1}{(√2+ √1)} + \frac{1}{(√3+ √2)} + \frac{1}{( √4+ √3)} + … + \frac{1}{( √25+ √24)}\)
\( =\frac{(√2-√1)}{[(√2+√1)(√2-√1)]} +\frac{(√3-√2)}{[(√3+√2) (√3-√2)]} +\frac{(√4-√3)}{[(√4+√3) (√4-√3)]} + … +\frac{(√25-√24)}{[(√25+√24)(√25-√24)]} \)
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We rationalize the denominator of each fraction to give
\(\frac{1}{(√2+ √1)} + \frac{1}{(√3+ √2)} + \frac{1}{( √4+ √3)} + … + \frac{1}{( √25+ √24)}\)
\( =\frac{(√2-√1)}{[(√2+√1)(√2-√1)]} +\frac{(√3-√2)}{[(√3+√2) (√3-√2)]} +\frac{(√4-√3)}{[(√4+√3) (√4-√3)]} + … +\frac{(√25-√24)}{[(√25+√24)(√25-√24)]} \)
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