Prove √a(n) Converges to 0 | Stuck on Proof

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Discussion Overview

The discussion revolves around proving that the sequence √a(n) converges to 0, given that a(n) converges to 0. Participants are exploring the implications of this convergence and seeking assistance with the proof process.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant states they are starting with the assumption that a(n) converges to 0 and introduces the concept of epsilon, indicating a need for clarification on the proof process.
  • Another participant reiterates the initial thought and questions the conditions of convergence, seeking to confirm whether a(n) indeed converges to 0.
  • There is a claim from one participant affirming that a(n) converges to zero.
  • One participant proposes proving that √a(n) is eventually less than 1/100 and then suggests a stronger condition of being less than 1/(1000000).

Areas of Agreement / Disagreement

Participants express uncertainty regarding the proof steps and conditions. While one participant asserts that a(n) converges to zero, the discussion remains unresolved regarding the specific proof of √a(n) converging to 0.

Contextual Notes

There is a lack of clarity on the definitions and conditions being used, particularly regarding the convergence of a(n) and the implications for √a(n). The proof steps are not fully articulated, leaving some assumptions unaddressed.

CoachBryan
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I've been messing with this proof for while and I'm stuck on this. I've started with a(n) converges to 0, let epsilon > 0, then there exists an n0 in N such that for all n >= n0.

I'm stuck here thus far. Any help? Thanks for your time.
 
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CoachBryan said:
I've been messing with this proof for while and I'm stuck on this. I've started with a(n) converges to 0, let epsilon > 0, then there exists an n0 in N such that for all n >= n0.

I'm stuck here thus far. Any help? Thanks for your time.
The rest of your thought is
For all n >= n0, ##\sqrt{a_n} < \epsilon##.

What are the given conditions? Is it an converges to 0? You have an = 0 in the title.
 
Mark44 said:
The rest of your thought is
For all n >= n0, ##\sqrt{a_n} < \epsilon##.

What are the given conditions? Is it an converges to 0? You have an = 0 in the title.

Yes it converges to zero
 
Can you prove that sqrt(an) is eventually less than 1/100 ?

How about that sqrt(an) is eventually less than 1/(1000000) ?
 

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