Problem 982
Use Euler-Maclaurin summation to find \(\displaystyle a)\ \sum_{k=1}^n k^5;\qquad\qquad b)\ \sum_{k=1}^n k^3(n-k)^3.\) Difficulty: 4. |
Problem 1006
How much work is required to elevate a mass from ground level to height \(\displaystyle h\)? To \(\displaystyle h=\infty\)? Difficulty: 4. |
Problem 1007
What curve is traced out by the centroids of the arc on the logarithmic spiral \(\displaystyle r=a\cdot e^{m\phi}\) \(\displaystyle (r=a,\psi=0)-P\) as \(\displaystyle P\) runs though all points on the spiral? Difficulty: 5. |
Problem 999
Prove that \(\displaystyle B(u,v) = \frac{\Gamma(u)\Gamma(v)}{\Gamma(u+v)}. \) for every \(\displaystyle u,v>0\). Difficulty: 9. |
Supported by the Higher Education Restructuring Fund allocated to ELTE by the Hungarian Government |