MathDB

6

Part of 2018 VTRMC

Problems(1)

Extrema of Difference of Sequences

Source: 2018 VTRMC P6

1/8/2023
For n∈Nn \in \mathbb{N}, define an=1+1/3+1/5+⋯+1/(2n−1)n+1a_n = \frac{1 + 1/3 + 1/5 + \dots + 1/(2n-1)}{n+1} and bn=1/2+1/4+1/6+⋯+1/(2n)nb_n = \frac{1/2 + 1/4 + 1/6 + \dots + 1/(2n)}{n}. Find the maximum and minimum of an−bna_n - b_n for 1≤n≤9991 \leq n \leq 999.
VTRMCcollege contestsSequencesextremamaximumminimum value