Question #4185

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

Expert's answer

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.

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.

## Comments

## Leave a comment