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Home » Question: Compute \( \sum_n=1^50 \frac1{\sqrtn + \sqrtn+1} \). - Dyverse

Question: Compute \( \sum_n=1^50 \frac1{\sqrtn + \sqrtn+1} \). - Dyverse

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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Thus, $\mathbf{v} = \left\langle -\frac{45}{14}, -\frac{3}{7}, \frac{1...
Verification: Cross product and dot product conditions are satisfied.
\boxed{\left\langle -\dfrac{45}{14}, -\dfrac{3}{7}, \dfrac{19}{14} \ri...
Question: In spherical coordinates, describe the surface defined by $\...
Solution: Convert to Cartesian coordinates using $\rho = \sqrt{x^2 + y...
\rho^2 = 2\rho \sin\phi \cos\theta \implies x^2 + y^2 + z^2 = 2x.
Rearranging:
x^2 - 2x + y^2 + z^2 = 0 \implies (x^2 - 2x + 1) + y^2 + z^2 = 1 \impl...
This is a sphere centered at $(1, 0, 0)$ with radius 1.
\boxed{\text{A sphere of radius 1 centered at } (1, 0, 0)}

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