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  then the sequence <xn> is
  • a)
    Convergent
  • b)
    Divergent
  • c)
    Oscillatory
  • d)
    None of the above
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
then the sequence <xn> isa)Convergentb)Divergentc)Oscillatoryd...
Let (X,d) be a metric space. A sequence in X is a function from N to X.
If ϕ : N → X is a sequence we write
(xn), (xn)n∈N or (x0,x1,...)
for ϕ, where xn = ϕ(n) is the nth term of the sequence ϕ = (x0,x1,...).
Sequences in R are called real sequences.
Definition 5.1. A sequence (xn) in X converges to x if for every neighborhood
U of x there exists N ∈ N such that
xn ∈ U for all n ≥ N.
In this case we write
xn → x or limn→∞
xn = x or limn
xn = x.
A sequence (xn) which does not converge is called divergent
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then the sequence <xn> isa)Convergentb)Divergentc)Oscillatoryd)None of the aboveCorrect answer is option 'B'. Can you explain this answer?
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