# Américo Tavares

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bio website problemasteoremas.wordpress.c… location Queluz, Portugal age 63 member for 3 years, 7 months seen 9 hours ago profile views 6,433

I am a retired electrical engineer, Portuguese. My math website is Problemas e Teoremas, in Portuguese, and is mostly about exercises in Calculus, such as this one, which is a translation from this answer of mine.

(A proof can be found in this answer.)

 56 Different methods to compute $\sum\limits_{n=1}^\infty \frac{1}{n^2}$ 30 Teenager solves Newton dynamics problem - where is the paper? 27 What is the result of infinity minus infinity? 25 Explain $\iint \mathrm dx\mathrm dy = \iint r \mathrm d\alpha\mathrm dr$ 25 Nice proofs of $\zeta(4) = \pi^4/90$?

# 24,105 Reputation

 +5 How do I prove this sum is not an integer +10 Integral by parts of this function +10 Finding root for the segment - found the formula but it doesn't work for some values - wrong formula? +10 Prove $1^2+2^2+\cdots+n^2 = {n+1\choose2}+2{n+1\choose3}$

# 37 Questions

 41 What is the importance of Calculus in today's Mathematics? 33 Is $\sqrt[3]{p+q\sqrt{3}}+\sqrt[3]{p-q\sqrt{3}}=n$, $(p,q,n)\in\mathbb{N} ^3$ solvable? 25 Asymptotic (divergent) series 20 Generalizing $\sum \limits_{n=1}^{\infty }n^{2}/x^{n}$ to $\sum \limits_{n=1}^{\infty }n^{p}/x^{n}$ 18 What does closed form solution usually mean?

# 144 Tags

 771 calculus × 198 218 sequences-and-series × 52 453 integration × 109 154 definite-integrals × 28 364 algebra-precalculus × 103 149 indefinite-integrals × 39 348 trigonometry × 93 146 limits × 40 306 homework × 92 127 multivariable-calculus × 39

# 16 Accounts

 Mathematics 24,105 rep 542118 TeX - LaTeX 723 rep 613 MathOverflow 246 rep 310 Area 51 176 rep 5 Physics 128 rep 6