Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Analysis Sequences & Series (Convergence)
Let (an) and (bn) be sequences of real numbers such that
\(\rm \left|a_n-a_{n+1}\right|=\frac{1}{2^n} \) and \(\rm \left|b_n-b_{n+1}\right|=\frac{1}{\sqrt{n}}\) for n ∈ ℕ.
Then
1
both (an) and (bn) are Cauchy sequences
2
(an) is a Cauchy sequence but (bn) need NOT be a Cauchy sequence
3
(an) need NOT be a Cauchy sequence but (bn) is a Cauchy sequence
4
both (an) and (bn) need NOT be Cauchy sequences