Mike Spivey
Reputation
31,814
238/100 score
4 85 177
Impact
~789k people reached

• 30 helpful flags
• 7,986 votes cast

 106 Can I use my powers for good? 95 Why is $1^{\infty}$ considered to be an indeterminate form 56 Anecdotes about famous mathematicians or physicists 44 How to sum this series for $\pi/2$ directly? 41 Proof that $\sum\limits_{k=1}^nk^2 = \frac{n(n+1)(2n+1)}{6}$?

Reputation (31,814)

 +5 Identity involving Euler's totient function: $\sum \limits_{k=1}^n \left\lfloor \frac{n}{k} \right\rfloor \varphi(k) = \frac{n(n+1)}{2}$ +10 Triple Euler sum result $\sum_{k\geq 1}\frac{H_k^{(2)}H_k }{k^2}=\zeta(2)\zeta(3)+\zeta(5)$ +10 A double series yielding Riemann's $\zeta$ +10 Why is $1^{\infty}$ considered to be an indeterminate form

Questions (27)

 65 Proving an alternating Euler sum: $\sum_{k=1}^{\infty} \frac{(-1)^{k+1} H_k}{k} = \frac{1}{2} \zeta(2) - \frac{1}{2} \log^2 2$ 61 Ways to evaluate $\int \sec \theta \, \mathrm d \theta$ 52 Combinatorial proof that $\sum \limits_{k=0}^n \binom{2k}{k} \binom{2n-2k}{n-k} (-1)^k = 2^n \binom{n}{n/2}$ when $n$ is even 47 Nice proofs of $\zeta(4) = \pi^4/90$? 44 Designing an Irrational Numbers Wall Clock

Tags (153)

 594 combinatorics × 102 249 statistics × 46 548 probability × 91 238 real-analysis × 23 380 binomial-coefficients × 62 192 optimization × 46 320 sequences-and-series × 43 154 linear-programming × 47 308 calculus × 30 154 analysis × 9

Accounts (17)

 Mathematics 31,814 rep 485177 MathOverflow 1,928 rep 1023 Theoretical Computer Science 306 rep 18 Quantitative Finance 201 rep 18 Cross Validated 163 rep 29