Sequences And Series Of Real Numbers -5 - Mathematics MCQ
20 Questions MCQ Test Topic-wise Tests & Solved Examples for Mathematics - Sequences And Series Of Real Numbers -5
then select the incorrect
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If f: N → R is a sequence, what is f(x) for each x ∈ n?
If < an > be a sequence such that 
then the sequence < bn > where bn = 
then A real number P is cluster point o f a sequence < an> if for any e > 0,
then which of the n following relation is correct?
If < xn > and < yn > are sequences o f real numbers, which of the following is/are true?
Consider the following statement
I. Every Cauchy sequence contains convergent subsequence
II. If a subsequence of a Cauchy sequence converges to a real numbers l, then the original sequence also converge to l.
III. Every monotone sequence contains a convergent subsequence.
IV. Every bounded sequence contains a convergent subsequence.
Select the correct answer using the codes given below:
If a sequence {xn} converge to x and xn > 0 for all n ∈ N, then
A sequence (x) of real numbers is defined as follows :
x0 = 1, x1 = 2 and
for n = 2, 3, 4, …. It follows that x2018 is
The limit superior and limit inferior of 
are respectively equal to
For any sequence < an>, <bn > of real numbers, we always have
Let <an> be a sequence of real numbers such that lim in f (an) = 0 and lim sup (an ) = T. Then,
The set of limit points of a bounded sequence is
If a sequence of real number has a cluster points, then
The inf and sup of the set 
are respectively
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