- #1

- 986

- 12

**{Sn} is convergent ---> {|Sn|} is convergent**

## Homework Statement

I need to prove that if {s

_{n}} is convergent, then {|s

_{n}|} is convergent.

## Homework Equations

*s*is convergent if for some

_{n}*s*and all

*ε > 0*there exists a positive integer

*N*such that |

*s*| <

_{n}- s*ε*whenever

*n*≥

*N*.

## The Attempt at a Solution

**Proof.**By contrapositive. Suppose {|s

_{n}|} is not convergent. Then for all

*s*there exists an

*ε > 0*such that ||

*s*| -

_{n}*s*|| ≥

*ε*for all

*n*.

... I need to somehow show that this implies that {

*s*} does not converge.

_{n}Maybe some fancy triangle inequality thing like

*ε*≤ ||

*s*| -

_{n}*s*| ≤ ||

*s*| -

_{n}*s*| + |

_{n}*s*-

_{n}*s*|

Wat do, PF?

Last edited: