Answer to Question #4185 in Real Analysis for Junel

Question

For any[i] b [/i]element in real numbers, prove that [i]lim (b/n)=0[/i]

Answer 1

Proof.We have to show that for any
e>0
there exist integer
N>0
such that for all
n>N
we have that
(*) |b/n| < e
Let N be any integer greater than |b/e|: N>|b/e|.
Then for any n>N we have that
n > N > |b/e|
whence
|b/n| < e,
which proves the statement.