### Answers (103)

 49 How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$? 10 Calculate $\sum_{k=1}^n \frac 1 {(k+1)(k+2)}$ 8 Prove that $\lim_{x\rightarrow 1}{\frac{x^n-1}{x-1}}=n$ for all integer n without L'Hôpital 6 Prove that if the square of a number $m$ is a multiple of 3, then the number $m$ is also a multiple of 3. 6 Proving that a convergent sequence has a unique limit

### Reputation (3,395)

 +5 Prove that ${\sum\limits_{n=1}^{\infty}}(-1)^{n-1} \frac{H_n}{n} = \frac{\pi^2}{12} - \frac12\ln^2 2$ +10 How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$? +10 How I can calculate $\sum_{n = 0}^{\infty}\frac{(-1)^n(2n + 1)}{n^2 + 1}$ +5 Closed form of $\int_{0}^{1}\int_{0}^{1}\frac{1}{1-\frac{xy}{2}}dxdy$

### Questions (28)

 85 Divisibility by 7 rule, and Congruence Arithmetic Laws 24 Proving that $\gamma = \int_{0}^{1} \!\!\int_{0}^{1} \!\frac{x - 1}{(1 - x y) \log(x y)} \, \mathrm{d}{x} \, \mathrm{d}{y}$. 15 Prove that ${\sum\limits_{n=1}^{\infty}}(-1)^{n-1} \frac{H_n}{n} = \frac{\pi^2}{12} - \frac12\ln^2 2$ 11 Integral involving square root of sine and cosine 6 Closed form of $\int_{0}^{1}\int_{0}^{1}\frac{1}{1-\frac{xy}{2}}dxdy$

### Tags (70)

 62 sequences-and-series × 18 23 integration × 26 53 power-series × 3 21 algebra-precalculus × 16 50 convergence × 2 18 limits × 7 49 faq 17 trigonometry × 11 38 calculus × 35 11 multivariable-calculus × 7

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