Question

Let (an) and (bn) be sequences of real numbers such that
$|a_n-a_{n+1}|=\frac{1}{2^n}$ and $|b_n-b_{n+1}|=\frac{1}{\sqrt{n}}$ for n ∈ $\N$.
Then

• A. both (an) and (bn) are Cauchy sequences
• B. (an) is a Cauchy sequence but (bn) need NOT be a Cauchy sequence
• C. (an) need NOT be a Cauchy sequence but (bn) is a Cauchy sequence
• D. both (an) and (bn) need NOT be Cauchy sequences

Answer 1

Answer: (B)

(an) is a Cauchy sequence but (bn) need NOT be a Cauchy sequence

Answer 2

The correct option is (B) : (an) is a Cauchy sequence but (bn) need NOT be a Cauchy sequence.