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If (xn) is a sequence of real numbers which converges to x then the sequence (sn) where
  • a)
    converges to 0
  • b)
    diverges
  • c)
    converges to x
  • d)
    None
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If (xn) is a sequence of real numbers which converges to x then the se...
(xn) converges to x implies that for every ∈ > 0 there exists an N such that
|xn – x| < ∈ for all n ≥ N 
We now divide the sum into those terms before N and those after N. We have
 
now 
which requires that n > C/∈ .
Thus if we let N = max{N, C/∈} then for all n ≥ N we have |sn – x| < 2∈ which proves that the sequence (sn) converges to x.
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If (xn) is a sequence of real numbers which converges to x then the sequence (sn) wherea)converges to 0b)divergesc)converges to xd)NoneCorrect answer is option 'C'. Can you explain this answer?
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