Basic Analysis I — Real Analysis · Problem 2.2.6

Sequences and Series — Jiri Lebl

Mathematics — Real Analysis · continuity-of-algebraic-operations

Problem

Let

x_n := \dfrac{1}{n^2}

and

y_n := \dfrac{1}{n}

. Define

z_n := \dfrac{x_n}{y_n}

and

w_n := \dfrac{y_n}{x_n}

. Do

\{z_n\}_{n=1}^\infty

and

\{w_n\}_{n=1}^\infty

converge? What are the limits? Can you apply Proposition 2.2.5? Why or why not?