Américo Tavares

Queluz, Portugal

problemasteoremas.wordpress.com

Age: 62

I'm a retired Portuguese electrical engineer.

You can contact me at acltavares[at]sapo[dot]pt

Blog Problemas Teoremas.

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What is the importance of Calculus in today's Mathematics?

calculus soft-question multivariable-calculus education asked Aug 17 '11 at 17:02

math.stackexchange.com

28 votes

Is $\sqrt[3]{p+q\sqrt{3}}+\sqrt[3]{p-q\sqrt{3}}=n$, $(p,q,n)\in\mathbb{N} ^3$ solvable?

algebra-precalculus number-theory elementary-number-theory diophantine-equations asked Apr 27 at 20:47

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24 votes

Asymptotic (divergent) series

real-analysis sequences-and-series reference-request divergent-series asked Mar 23 '12 at 15:21

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20 votes

Generalizing $\sum \limits_{n=1}^{\infty }n^{2}/x^{n}$ to $\sum \limits_{n=1}^{\infty }n^{p}/x^{n}$

calculus sequences-and-series asked Sep 8 '10 at 23:31

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17 votes

What does closed form solution usually mean?

soft-question closed-form asked Nov 6 '10 at 20:09

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16 votes

Exercise from Comtet's Advanced Combinatorics: prove $27\sum_{n=1}^{\infty }1/\binom{2n}{n}=9+2\pi \sqrt{3}$

combinatorics sequences-and-series binomial-coefficients asked Nov 12 '10 at 21:12

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15 votes

How to draw these diagrams (closed contours) using TikZ or PSTricks?

tikz-pgf pstricks asked Oct 18 '12 at 11:34

tex.stackexchange.com

12 votes

How to prove $\cos \frac{2\pi }{5}=\frac{-1+\sqrt{5}}{4}$?

geometry trigonometry euclidean-geometry asked Oct 24 '10 at 16:57

math.stackexchange.com

11 votes

How to typeset a continued fraction in the following format?

fractions asked Sep 19 '12 at 13:58

tex.stackexchange.com

10 votes

How do I prove the partial denominators formula of the Bauer-Muir transformation of a generalized continued fraction?

number-theory sequences-and-series continued-fractions computational-mathematics asked Sep 14 '10 at 10:13

math.stackexchange.com

Top Answers

Different methods to compute $\sum\limits_{n=1}^\infty \frac{1}{n^2}$

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Teenager solves Newton dynamics problem - where is the paper?

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What is the result of infinity minus infinity?

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Explain $\iint \mathrm dx\mathrm dy = \iint r \mathrm d\alpha\mathrm dr$

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Adding powers of $i$

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Nice proofs of $\zeta(4) = \pi^4/90$?

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Integral of $\frac{1}{(1+x^2)^2}$

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What is Jacobian Matrix?

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Continued fraction for $\frac{1}{e-2}$

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Is there a way to determine how many digits a power of 2 will contain?

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Tall fraction puzzle

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How to find roots of $X^5 - 1$?

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Inverse of $y = x^3 + x$?

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How to prove by arithmetical means that $\sum\limits_{k=1}^\infty \frac{((k-1)!)^2}{(2k)!} =\frac{1}{3}\sum\limits_{k=1}^{\infty}\frac{1}{k^{2}}$

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Compute $\int \frac{\sin(x)}{\sin(x)+\cos(x)}\mathrm dx$

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Solve trigonometric equation: $1 = m \; \text{cos}(\alpha) + \text{sin}(\alpha)$

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Proving $\int_{0}^{+\infty} e^{-x^2} dx = \frac{\sqrt \pi}{2}$

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Prove: $\int_0^1 \frac{\ln x }{x-1}=\sum_1^\infty \frac{1}{n^2}$

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Computing $\zeta(6)=\sum\limits_{k=1}^\infty \frac1{k^6}$ with Fourier series.

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Deriving a trivial continued fraction for the exponential

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Name for $(1-x)$?

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Prove $\frac{1}{1 \cdot 3} + \frac{1}{3 \cdot 5} + \frac{1}{5 \cdot 7} + \cdots$ converges to $\frac 1 2 $

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Why is $\frac{k \cdot(\sin (A) + \sin(B))}{k \cdot(\sin(A) -\sin(B))} = \frac{a+b}{a-b}$ valid in a triangle?

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Understanding Limits of Integration in Integration-by-Parts

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How to calculate $\int_0^{2\pi} \sqrt{1 - \sin^2 \theta}\;\mathrm d\theta$

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Is there a more efficient method of trig mastery than rote memorization?

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Help finding integral: $\int \frac{dx}{x\sqrt{1 + x + x^2}}$

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System of equations: $x^2+y=7, y^2+x=11$

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Which Fourier series formula is correct

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How i can determine: $\lim_{x\to1} \frac{x^{\frac{1}{3}}-1}{x^{\frac{1}{4}}-1}$?

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