user296113's user avatar
user296113's user avatar
user296113's user avatar
user296113
  • Member for 8 years, 4 months
  • Last seen more than 2 years ago
32 votes
Accepted

Prove that the infinite sum $\sum_{n=1}^{\infty} \frac{F_{n}}{ 10 ^ n }$ converges to a rational number

13 votes
Accepted

Prove that a symmetric matrix with a positive diagonal entry has at least one positive eigenvalue

13 votes
Accepted

$s_n = \sum_{k=1}^{n} a_k$ and $\sum_{n=1}^{\infty} a_n = \infty$ imply $\sum_{n=1}^{\infty} \frac{a_n}{s_n^2}$ converges!

11 votes

How do I show the series $\sum{\frac{1}{\log(n)^{\log(n)}}}$ converges?

9 votes

How many entries in a symmetric matrix can be chosen independently?

8 votes
Accepted

Converge? $\sum_{k=1}^{\infty}\frac{ \sin \left(\frac{1}{k}\right) }{k} $

8 votes
Accepted

Determine matrix of linear map

8 votes
Accepted

Parametric representation of orthogonal matrices

7 votes
Accepted

Calculate the determinant of this $5 \times 5$ matrix

7 votes
Accepted

Linear transformation from $\mathbb{R}^3 \to \mathbb{R}$

6 votes

Assume $E[X^2]=20$. Find the mean and variance of $X$ if the mean and variance are equal.

6 votes

Taylor series for $\ln(a-x)$ centered at $x=0$

6 votes

$\mathbb{P}(B) = 1 \implies \mathbb{P}(A \mid B) = \mathbb{P}(A)$

6 votes
Accepted

Alternating series: $\sum\limits_{n= 1}^{\infty} (-1)^{n-1} \frac{\ln(n)}{n}$ convergence?

6 votes
Accepted

How to find a formula for $\sum_{a=1}^n \frac{a}{(a+1)!}$ for a specific n

6 votes
Accepted

Prove using mean value theorem.

6 votes
Accepted

Proving $d(x,A)\le d(x,y)+d(y,A) $

6 votes

Let $s_{n} := 1 + 1/2 + \cdots + 1/n - \ln(n+1)$ and show that $s_{n} \leq 1 - 1/(n+1)$.

6 votes
Accepted

Do exist an injective linear map from $\mathbb{R}^5\rightarrow\mathbb{R}^4$

5 votes

Evaluate $\displaystyle{\lim_{n\to \infty}}(1-\frac 12 +\frac 13 - \frac 14 + \cdots + \frac{1}{2n-1}-\frac{1}{2n}) $

5 votes
Accepted

Does $\operatorname{tr} (A)=0$ imply $\operatorname{tr} (A^3)=0$?

5 votes
Accepted

How to prove $\dim E=\dim E^*$?

5 votes
Accepted

Double summation identity

5 votes

$\lim\limits_{x\to \infty} \frac{1}{\ln(x+1)-\ln(x)}-x$

5 votes

Show that if $A$ is a nilpotent matrix then there exists $k\leq n$ s.t. $A^k=0$ without using Cayley-Hamilton

5 votes

Sequence $a_n$ which doesn't converge but $a_n^2-4a_n$ converges to $0$

5 votes

Why does convergence to zero in two norms imply equivalence?

5 votes
Accepted

Series Converging Uniformly

5 votes

Proof that $\dim(U_1+U_2) = \dim U_1 + \dim U_2 - \dim(U_1\cap U_2)$

5 votes
Accepted

a self adjoint in complex vector space

1
2 3 4 5
9