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1. The problem statement, all variables and given/known data

I need to prove that if {s_{n}} is convergent, then {|s_{n}|} is convergent.

2. Relevant equations

sis convergent if for some_{n}sand allε > 0there exists a positive integerNsuch that |s| <_{n}- sεwhenevern≥N.

3. The attempt at a solution

Proof.By contrapositive. Suppose {|s_{n}|} is not convergent. Then for allsthere exists anε > 0such that ||s| -_{n}s|| ≥εfor alln.

..... 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?

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# Homework Help: {Sn} is convergent -> {|Sn|} is convergent

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