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Infinite series questions for calculus?
Which of the following statements are true?
I. The limit of the nth term of a divergent sequence is always infinity.
II. Every bounded sequence is convergent.
III. If the limit of a series is equal to 0 then the series is convergent.
I only
II only
III only
None of these
All of these
Determine which one of the following tests can be used to show that the harmonic series diverges.
Geometric Series Test
nth term test
Telescopic Series Test
Integral Test
None of these
Im pretty sure the first answer is II only and the last answer is integral test. Please just help me out!
1 Answer
- RockItLv 77 years agoFavorite Answer
None of these
Integral test, at some point, the sequence continues to get smaller and smaller so we can take the integral of the remainder which is the ln function. The ln function diverges.
no, II only is not correct, Proof by Counter Example: the bounded sequence (-1)^k does not converge. It diverges because it oscillates.
