### Answers (126)

 17 Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$ 14 How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$? 13 Proving $\lim_{x\to\infty}\frac{\sqrt x\cos(x-x^2)}{x+1} = 0.$ 11 How can I calculate $\alpha=\arccos\left(-\frac{1}{4}\right)$ without using a calculator? 8 Compute : $\int\frac{x+2}{\sqrt{x^2+5x}+6}~dx$

### Reputation (3,524)

 +10 How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$? +10 Proving that ${x +y+n- 1 \choose n}= \sum_{k=0}^n{x+n-k-1 \choose n-k}{y+k-1 \choose k}$ -2 Prove that $6p$ is always a divisor of $ab^{p} - ba^{p}$. +10 Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$

### Questions (38)

 31 How can I calculate $\alpha=\arccos\left(-\frac{1}{4}\right)$ without using a calculator? 10 Proving that ${x +y+n- 1 \choose n}= \sum_{k=0}^n{x+n-k-1 \choose n-k}{y+k-1 \choose k}$ 8 Book recomendation for Elliptic-curve cryptography 5 smallest number of socks to guarantee that the selection contains at least $10$ pairs 4 Determine sum of the series $\sum_{k=1}^\infty\frac{1}{n(n+1)(n+2)}$ [duplicate]

### Tags (127)

 41 calculus × 29 19 elementary-number-theory × 9 35 sequences-and-series × 23 19 gcd-and-lcm × 3 34 faq × 3 18 indefinite-integrals × 10 33 integration × 24 17 convergence-divergence × 4 20 divisibility × 4 16 limits × 13

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 1390 Visually stunning math concepts which are easy to explain 924 Can I use my powers for good? [closed] 797 The staircase paradox, or why $\pi\ne4$ 663 What was the first bit of mathematics that made you realize that math is beautiful? (For children's book) [closed] 478 How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?

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