# MathFacts

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bio website fatosmatematicos.blogspot.com location Brazil age 42 member for 3 years, 5 months seen Dec 11 at 19:17 profile views 165

Discrete Mathematics, Geometry, Calculus, Analitic Number Theory, Precalculus.

 6 Prove that $\lim_{x\rightarrow 1}{\frac{x^n-1}{x-1}}=n$ for all integer n without L'Hôpital 5 How can I evaluate $\sum_{n=0}^\infty (n+1)x^n$ 5 Evaluate the limit: $\lim_{x\to \infty}$ 4 Evaluating $\int x^2 \sqrt{x^2-1} dx$ 4 Different Definitions Of The Sine Function

# 1,731 Reputation

 +40 How can I evaluate $\sum_{n=0}^\infty (n+1)x^n$ +10 Proving that $\displaystyle \gamma = \int_{0}^{1} \!\!\int_{0}^{1} \!\frac{x - 1}{(1 - x y) \log(x y)} \, \mathrm{d}{x} \, \mathrm{d}{y}$. +15 Second order homogenous non-linear DE: $3(x')^2 - 2x''x=0$ +10 Calculate $\sum_{k=1}^n \frac 1 {(k+1)(k+2)}$

# 13 Questions

 14 Proving that $\displaystyle \gamma = \int_{0}^{1} \!\!\int_{0}^{1} \!\frac{x - 1}{(1 - x y) \log(x y)} \, \mathrm{d}{x} \, \mathrm{d}{y}$. 8 Prove that $\displaystyle{\sum_{n=1}^{\infty}}(-1)^{n-1} \dfrac{H_n}{n} = \dfrac{\pi^2}{12} - \dfrac{1}{2}\ln^2 2$ 6 Integral involving square root of sine and cosine 3 How can I find the volume of prism: $V = \frac{(a + b + c)Q}{3}$ 3 Closed form for the sum: $\sum_{n=1}^{\infty}\frac{1}{n(n + 1/3)}$ [duplicate]

# 65 Tags

 29 calculus × 23 10 sequences-and-series × 12 18 integration × 15 9 trigonometry × 7 18 algebra-precalculus × 14 9 power-series × 3 13 limits × 5 7 differential-equations × 11 11 multivariable-calculus × 7 6 convergence × 2

# 2 Accounts

 Mathematics 1,731 rep 518 TeX - LaTeX 116 rep 4