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How do you show that if a(n) >= 0 for all n in N and a(n) = 0, then √a(n) Converges to 0

  1. Nov 5, 2014 #1
    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.
  2. jcsd
  3. Nov 5, 2014 #2


    Staff: Mentor

    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.
  4. Nov 5, 2014 #3
    Yes it converges to zero
  5. Nov 5, 2014 #4
    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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