Douglas Zare
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 30 Simple probability question, balls and bins 22 How to express $(1+x+x^2+\cdots+x^m)^n$ as a power series? 15 Prove that $\lfloor \sqrt{p} \rfloor + \lfloor \sqrt{2p} \rfloor +…+ \lfloor \sqrt{\frac{p-1}{4}p} \rfloor = \dfrac{p^2 - 1}{12}$ 13 A question about calculators (are $\sin^2 49^{\circ}$ and $\cos^2 49^{\circ}$ irrational?) 9 What does the symbol $\otimes$ mean?

### Reputation (2,495)

 +20 Prove that $\lfloor \sqrt{p} \rfloor + \lfloor \sqrt{2p} \rfloor +…+ \lfloor \sqrt{\frac{p-1}{4}p} \rfloor = \dfrac{p^2 - 1}{12}$ +10 Sum of independent Binomial random variables with different probabilities? +10 What does the symbol $\otimes$ mean? +10 First exit time for Brownian motion without drift

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### Tags (46)

 70 probability × 13 14 stochastic-processes × 4 33 real-analysis × 3 13 trigonometry 22 power-series 13 calculator 21 elementary-number-theory × 3 12 notation × 2 16 sequences-and-series × 3 11 combinatorics × 6

### Accounts (9)

 MathOverflow 18,028 rep 45386 Cross Validated 6,025 rep 11433 Mathematics 2,495 rep 714 Stack Overflow 1,579 rep 38 Theoretical Computer Science 286 rep 4