Proving a Sequence Converges Advanced Calculus Example

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Proving a Sequence Converges Advanced Calculus Example.
  1. The Math Sorcerer
  2. Math
  3. advanced calculus
  4. Calculus (Field Of Study)
  5. Mathematics (Field Of Study)
  6. Sequence
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Комментарии
Автор

I'm not sure how the last inequality follows at 2:07. What if n = 1? Then 4/sqrt(n) + 2/n = 4/sqrt(n) + 2/sqrt(n) instead of being less than.

crm
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Does capital 'N' have to be a positive integer? I'm using Analysis: with introduction to proof by Lay, and he writes that a sequence converges provided that for each epsilon > 0, there exists a real number 'N' such that for any natural number 'n', n > N implies that | s_n - s | < epsilon.

mmeixner
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at 2:00 why don't you square root the top number as well? why only the n?

roshnipatel
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At 6:17, shouldn't it be only 'less than' instead of 'less than equal to' ?

harleendiaries
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What are the n's for and where do they relate and why do they matter???

kagayakuangel
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idk why we had to add 1 tho. otherwise great explanation

sundaymanali
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I don't see how your +1 thing is necessary... n needs to be greater than (6/eps)^2. As these are sequences were are dealing with n needs to be greater than the next integer greater or equal to (6/eps)^2. That integer is ceil((6/eps)^2). I don't see where we need the +1 in that.

ElizaberthUndEugen