Which of the following statements are true if and only if the sequence of real numbers {n} is a Cauchy sequence? Mark all that apply. D (VE > 0)(ZM e N)(n > M)(Vk > M)(2n – k| < E) (Ve > 0) (M € N) (\n ≥ M)(x₂ − xn+1 < €) □ (Vp € N) (Vq € N) (M € N) (Vn > M)(√k ≥ M)(\xn− xk| 0) (3M € N) (n ≥ M)(√k ≥ M)(xn - xk| < €) (3 > | 1+WxWx) (NA) (NWE) (0 < ³A) O
Which of the following statements are true if and only if the sequence of real numbers {n} is a Cauchy sequence? Mark all that apply. D (VE > 0)(ZM e N)(n > M)(Vk > M)(2n – k| < E) (Ve > 0) (M € N) (\n ≥ M)(x₂ − xn+1 < €) □ (Vp € N) (Vq € N) (M € N) (Vn > M)(√k ≥ M)(\xn− xk| 0) (3M € N) (n ≥ M)(√k ≥ M)(xn - xk| < €) (3 > | 1+WxWx) (NA) (NWE) (0 < ³A) O
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Transcribed Image Text:Which of the following statements are true if and only if the sequence of real numbers
{n} is a Cauchy sequence?
Mark all that apply.
D (VE > 0)(ZM e N)(n > M)(Vk > M)(2n – k| < E)
(Ve > 0) (M € N) (\n ≥ M)(x₂ − xn+1 < €)
□ (Vp € N) (Vq € N) (M € N) (Vn > M)(√k ≥ M)(\xn− xk| <p/q)
(VE > 0) (3M € N) (n ≥ M)(√k ≥
M)(xn - xk| < €)
(3 > | 1+WxWx) (NA) (NWE) (0 < ³A) O
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