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Home » $\1,2\, \3,4\$ - High Altitude Science

$\1,2\, \3,4\$ - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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\frac{\frac{1}{3}}{1 - \frac{1}{3}} = \frac{\frac{1}{3}}{\frac{2}{3}}...
So the sum is \( 3 \cdot \frac{1}{2} = \frac{3}{2} \).
Thus, the minimum value is \( \boxed{\frac{3}{2}} \).
Question: Compute \( \sum_{n=1}^{50} \frac{1}{\sqrt{n} + \sqrt{n+1}} \...
Solution: Consider the general term:
\frac{1}{\sqrt{n} + \sqrt{n+1}}
Rationalize the denominator by multiplying numerator and denominator b...
\frac{1}{\sqrt{n} + \sqrt{n+1}} \cdot \frac{\sqrt{n+1} - \sqrt{n}}{\sq...
\sum_{n=1}^{50} \left( \sqrt{n+1} - \sqrt{n} \right) = (\sqrt{2} - \sq...
\sqrt{51} - \sqrt{1} = \sqrt{51} - 1

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