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Debu
  • Member for 3 years, 10 months
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8 votes
2 answers
712 views

Question regarding multiplication table of group of odd order.

4 votes
1 answer
64 views

$\limsup_{n \to \infty} \Big|\frac{a_{n+1}}{a_{n}}\Big| > 1$ does not imply the divergence of $\sum a_{n}$

4 votes
1 answer
72 views

Finding the limiting distribution of $T_{n}/S_{n}$ as n tends to infinity

3 votes
1 answer
75 views

Convergence of the sequence $x_{n} = \int_{1}^{n}\frac{\cos t}{t^{2}}$ as n tends to infinity.

3 votes
0 answers
74 views

(Soft-question) Need a guidance and some truth [closed]

2 votes
0 answers
56 views

Necessary and sufficient condition for almost sure convergence of a series of i.i.d. random variables.

2 votes
1 answer
53 views

Iterative application of continuous function $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $\lim_{n \to \infty}f^{n}(x)$ exists $\forall x$.

2 votes
4 answers
94 views

Convergence/divergence of the series $\sum\frac{n}{(n+1)^{2}}$

1 vote
1 answer
70 views

Is $x = 0$ the extremum of the function $e^{-x}\sum_{i=0}^{n}\frac{x^{i}}{i!}$, $n \geq 4$

1 vote
2 answers
79 views

Coloring 4 walls of a room with 4 colours such that no adjacent walls have same colours.

1 vote
1 answer
19 views

Given that a homogenous system of linear equation in three variable has a non trivial solution, evaluate the following expression.

1 vote
2 answers
42 views

Sum of $Y$ i.i.d Binomial Random variables $(n,p)$, where $Y$ follows poisson distribution

1 vote
1 answer
74 views

Convergence of the series $\sum_{n}\frac{3^{n}n!}{7 \cdot 10 \cdot 13 \cdots (3n+4)}x^{n}$, $x >0$

1 vote
0 answers
29 views

Why doesn't the following idea prove the statement "If $A_{1}, A_{2}$ are regular languages then so is $A_{1}+A_{2}$"

1 vote
0 answers
39 views

$x_{1} = \sqrt{2}$ and $x_{n+1} = \sqrt{2+x_{n}}$. Show that the sequence converges and find it's limit. [duplicate]

1 vote
3 answers
96 views

If $P$ and $Q$ are two propositions, then what can be said about the expression $(P \wedge(P \to Q)) \to Q$

1 vote
1 answer
44 views

Inclusion of set $A$ in set $B$ or vice versa, where A and B are defined as follows:

1 vote
1 answer
75 views

Given that $f(x) = f(\frac{x}{1-x}) \forall x \ne 1$, and $f$ is continuous at $0$. Find all such $f$.

0 votes
1 answer
18 views

Put the given numbers in increasing order.

0 votes
0 answers
12 views

Finding limit of a sequence $\sqrt{n}\left(A_{n+1}-A_n\right)$ [duplicate]

0 votes
0 answers
25 views

Let $a_{n} > 0$ and $\sum a_{n}$ converges. Prove that $\forall p > \frac{1}{2}$ , $\sum \frac{\sqrt{a_{n}}}{n^{p}}$ converges. [duplicate]

0 votes
1 answer
28 views

How to show that column span of $B$ and $BB^{'}$ are same. [duplicate]

0 votes
0 answers
52 views

$\psi,f:\Bbb R\to\Bbb R$ are continuous, $\psi=0$ outside $[0,1]$, $\int\psi=1$. $\lim_{n\to\infty}n\int_0^{100}f(x)\psi(nx)dx=?$ [duplicate]

0 votes
2 answers
34 views

A $\in$ $M_{4 \times 4}$. Let $A$ and $adjA$ (transpose of cofactor matrix of A) be non null matrix, and detA = 0. Find rank of A

0 votes
1 answer
49 views

If $B$ is a $n \times n$ matrix, then is the column space of $B$ and $BB^{'}$ same?

0 votes
0 answers
48 views

Let $\{a_{n}\}$ be a positive decreasing sequence such that $\lim_{n\to \infty}na_{n}$ goes to 0. Does it follow that $\sum a_{n}$ converges?

0 votes
0 answers
76 views

$A,B \in GL_{n}$. Let $f(x) = det(xA+(1-x)B)$. Then conclude $f$ is a non constant polynomial.

0 votes
1 answer
38 views

Maximizing an expression which involved $p$ which probability of a vaccine causing side effect.

0 votes
0 answers
25 views

Prove that edge connectivity of a complete graph with $n$ vertices is $n-1$

0 votes
0 answers
12 views

Prove that minimal disconnecting set is a cut. (Definitions included in the body).