Let be the statement '' and be the statement 'the sequence converges'. Which of the following is correct? (Here is a real number.)

Answer and explanation

Correct answer: C. is a sufficient but not a necessary condition for

  1. Step 1: If then , so the sequence converges: .
  2. Step 2: But gives the constant sequence , which converges although fails: .
Answer
is a sufficient but not a necessary condition for .
Why not the others: The value is the only boundary case; oscillates and diverges, so alone shows that is not necessary.

Practise more Necessary and sufficient conditions on a parameter.

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