Top network posts

• 9 Evaluate $\sum\limits_{k=0}^n(-1)^{n+k}{n\choose k}{ {n+k}\choose n} \frac{1}{k+2}$
• 8 Prove that $512^3 + 675^3 + 720^3$ is a composite number
• 7 Is the sequence $x_n=\dfrac{1}{\sqrt{n}}\left(1+\dfrac{1}{\sqrt{2}}+\dfrac{1}{\sqrt{3}}+\ldots+\dfrac{1}{\sqrt{n}}\right)$ monotone?
• 7 I need a relation which is not reflexive, not symmetric, and not transitive
• 5 True or False: The circumradius of a triangle is twice its inradius if and only if the triangle is equilateral.
• 5 Evaluate $\sum_{j=0}^n(-1)^{n+j}{n\choose j}{{n+j}\choose j}\frac{1}{(j+1)^2}$
• 5 Apostol (6.25.40): Find $\int {x^{-2}}\sqrt{2 - x - x^2} dx$
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