Theory check

Calculus Level 4

Which of these statements are always true?

  • A: If \( \{ a_n \} \) is Cauchy sequence, then the sequence converges in any metric space
  • B: If \( \{ b_n \} \) bounded sequence, then it must have a sub-sequence that converges
  • C: If \( \{ c_n \} \) is strictly monotonic sequence, then it converges to its infimum or supremum
  • D: If \( \{ d_n \} \) is sequence that converges, every sub-sequence of \( \{ d_n \} \) converges as well
  • E: If sequences \( \{ x_n \} \) and \( \{ y_n \} \), satisfy for each \( n \) : \( x_n > y_n \). Then, the following will be satisfied as well: \(\ \lim_{x\to\infty } x_n > \lim _{ y \rightarrow \infty }{ y_n } \)
×

Problem Loading...

Note Loading...

Set Loading...