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Theta
  • Member for 7 years, 10 months
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7 votes
2 answers
2k views

Convergence of a series in a Hilbert space

7 votes
6 answers
670 views

Prove that $\lim\limits_{n\rightarrow\infty} \left(1+\frac{1}{a_{n}} \right)^{a_{n}}=e$ if $\lim\limits_{n\rightarrow\infty} a_{n}=\infty$

6 votes
2 answers
8k views

Show that the operator is invertible

5 votes
1 answer
183 views

A linear operator $Tx=(x_1,x_1+x_2,x_1+x_3,\dots)$ between $c_0$ and $c$ and its norm

5 votes
1 answer
1k views

The norm of $(Af)(x)=\int_0^x f(t)\,dt$

3 votes
2 answers
193 views

Uniqueness of a vector with the minimal Euclidean norm

2 votes
1 answer
172 views

A sum of squared binomial coefficients

2 votes
2 answers
144 views

The expansion of $(a+b+c+d)^{20}$ [closed]

2 votes
8 answers
146 views

Find $\lim\limits_{n \rightarrow \infty}n\bigg(\cos \bigg(\frac {1}{\sqrt n} \bigg) - 1\bigg)$

2 votes
5 answers
288 views

No L' Hospital $ \lim_{x \rightarrow 0} \left (1+\frac {1} {\arctan x} \right)^{\sin x}$ and $ \lim_{x \rightarrow 0} \frac {\tan ^7 x} {\ln (7x+1)} $

1 vote
3 answers
546 views

A simpler form of $\sin{(\frac{1}{2}\arcsin{x})}$

1 vote
1 answer
297 views

Convergence of an improper integral with a parameter

1 vote
1 answer
165 views

A minimum of a function in a normed space with inner product

1 vote
1 answer
1k views

Show that the operator $(Af)(x)=\int_0^x f(t) \, dt$ is continuous and find the norm

1 vote
2 answers
80 views

$P(X_{1}+1>X_{2})$ for exponential variables

1 vote
0 answers
227 views

Bounded linear integral operator and its norm [duplicate]

1 vote
2 answers
1k views

Removable singularities and an entire function

0 votes
1 answer
443 views

Minimum distance between functions in $L^{2}(-\pi, \pi)$

0 votes
2 answers
902 views

Show that $l^1$ is not a closed linear subspace of $l^\infty$

0 votes
3 answers
603 views

Solving a recurrence relation with n squared

0 votes
2 answers
2k views

Permutations of n numbers with no odd numbers next to each other

0 votes
2 answers
1k views

Number of spanning trees in cycle graphs joined together

0 votes
5 answers
70 views

Is multiplication an operation in the given set of matrices?

0 votes
1 answer
452 views

Behaviour of a complex series on the boundary of the disk of convergence

0 votes
2 answers
222 views

Proof that a circle can be circumscribed around a quadrilateral [duplicate]

-1 votes
2 answers
200 views

Leg bisectors in a trapezoid and angle equality