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Basic limits

Basic limits

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Basic terminology and definitions for limits of sequences

Items (15)

  • A sequence of numbers is defined for:

    every natural number

  • A sequence is bounded below if:

    the sequence is positive

  • A sequence is bounded above if:

    there exists a value which is greater than every value the sequence generates

  • A sequence increases monotonically if:

    a(k) < a(k+1)

  • A sequence converges if and only if the sequence is bounded and is monotonic increasing or decreasing


  • The sequence sin(n) has:

    Infinite points for which the sequence is positive and infinite points for which it is negative

  • A sequence converges if it is bounded and is monotonic


  • The supremum of a set of values is the:

    The least upper bound

  • The infimum of a set of values is the:

    The greatest lower bound

  • A monotonic decreasing sequence converges to its:


  • The sequence 1/n converges to (what is the limit of 1/n)?


  • The sequence ((-1)^n)/n converges to


  • The sequence (-1)^n converges to

    The series does not converge

  • The limit, L, of a sequence is the value for which

    for every value e, there exist a value N, such that for all n>N |a(n) - L | < e

  • A sequence can converge to two different points