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
- Step 1: If then , so the sequence converges: .
- 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.
Free questions with an explanation for every one, and full timed TMUA mock tests.
More Necessary and sufficient conditions on a parameter questions
- Let be the statement '' and be the statement ' for every real '. Which of the following is correct?…
- Let be the statement '' and be the statement ' for every real '. Which of the following is correct?…
- Let be the statement '' and be the statement 'the function has no stationary point'. Which of the following…
- Let be the statement '' and be the statement 'the line meets the parabola at two distinct point…