MathDB
Today's calculation of Integral 379

Source: 1986 Yamaguchi University entrance exam/Science

October 16, 2008
calculusintegrationlimitcalculus computations

Problem Statement

Let α, r \alpha ,\ r be real numbers such that r>1, r≠3, r≠4 r > 1,\ r\neq 3,\ r\neq 4. Find the values of α, r \alpha ,\ r such that \lim_{n\to\infty} \sum_{k \equal{} 1}^n \frac {n^{\alpha}}{(n \plus{} k)^{r}} \equal{} \frac {r \minus{} 3}{(r \minus{} 1)(r \minus{} 4)}.
Back to ProblemsView on AoPS