Lebl-Basic-Analysis-I · Problem 2.1.21

Sequences and Series

Mathematics · sequences-and-limits

Problem

Show that the 3-tail of the sequence defined by

x_n := \dfrac{n}{n^2+16}

is monotone decreasing. Hint: Suppose

n \geq m \geq 4

and consider the numerator of the expression

x_n - x_m