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Zaragosa
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22 votes
Accepted

Proving $\sum_{n=1}^{99}\frac{\sqrt{n+1}-\sqrt{n}}{2n+1}\lt\frac9{20}$

10 votes
Accepted

Help me on this Equation

6 votes
Accepted

Evaluate the limit of $(1/n)( \sin (\phi/n) + \sin (2\phi/n) + … + \sin ((n-1)\phi/n))$

6 votes
Accepted

Is there any formula for $\operatorname{arctan}{(a+b)}$

6 votes

Dividing numerator and denominator of integrand in definite integral

3 votes
Accepted

Why is this inequality regarding squares true?

3 votes
Accepted

(Unique) OR (unique + nontrivial) prime ideal

3 votes
Accepted

Question regarding the limit of $f(x)= \sqrt{x+1} - \sqrt{x}$ using the MVT

2 votes

How to integrate $\int \frac{dx}{x\sqrt{x^4-1}}$?

2 votes

Determining if the sequence $\frac{(2n+3)!}{(n+1)!}$ is monotonic and bounded

2 votes
Accepted

Number of roots of a polynomial in respect to a variable

2 votes
Accepted

A detail in proposition 2.4 of Atiyah-MacDonald

2 votes
Accepted

For what $\lambda$ are the vectors linearly dependent?

2 votes

Prove $\sqrt{\sum^n_{k=1}(a_k+b_k)^2} \leq \sqrt{\sum^n_{k=1}(a_k)^2} + \sqrt{\sum^n_{k=1}(b_k)^2}$.

2 votes
Accepted

The metric $g=dx^2+\cosh^2(x)dy^2$ is complete

2 votes
Accepted

$\frac{(a+b)(b+c)(c+a)}{8abc}\ge\sqrt[8]{\left(\frac{a}{b}+\frac{b}{a}-1\right)}$

2 votes
Accepted

Prove that $r(P^n) =P$ , P is prime ideal

2 votes

Derivative of power function when power itself is a function

2 votes
Accepted

What is the right codomain for arccos(x)?

2 votes
Accepted

If $f: I \to R$ is continuous and I is sequentially compact. Prove that if $\lim_{n\to\infty}f(x_n) = L $ then $\exists x \in I$ s.t $f(x) = L$ Verify

2 votes
Accepted

$\sum_{k=1}^n k^{2m}$ is factorized by 2n+1

2 votes
Accepted

How to prove $(1+q)^n \geq1+qn$ for all $\mathbb{N}$ with $q>0$

1 vote

Prove that $\sum_{k=0}^{n} \frac{1}{4^{k}}=\frac{4}{3}-\frac{1}{3 \cdot 4^{n}}$ converges to $\frac{4}{3}$ using the $\varepsilon-N$ proof

1 vote

Prove that $A$ is connected

1 vote
Accepted

If $fg=gf$ show that $\exp(f+g) = \exp(f)\exp(g)$.

1 vote
Accepted

Laplace transform of $y(t)$

1 vote

Limits and trigonometry. What am I doing wrong?

1 vote
Accepted

show that the series is descending

1 vote
Accepted

$r(I) =1 \iff I =1$

1 vote

The solutions of a linear differential equation!