Basic Analysis I — Real Analysis · Problem 2.1.21

Sequences and Series — Jiri Lebl

Mathematics — Real Analysis · tail-of-a-sequence

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