Michael Biro
Reputation
5,830
Top tag
Next privilege 10,000 Rep.
Access moderator tools
7 19
Impact
~76k people reached

 16 Prove by induction that an expression is divisible by 11 12 Prove that $1+ \frac{1}{x^4} \geq \frac{1}{x} + \frac{1}{x^3}$ 8 Is the series $\sum_{n=1}^\infty\frac{n-1}{n+\ln n}$ convergent? 8 Probability of getting ten unique numbers 8 Solve $n + n/2 + n/4 + n/8 + \dots$ up to $\log n$ terms

### Reputation (5,830)

 +10 Prove that if two open balls in a vector space are equal then their radii and centres are equal +10 How to find limit of a sequence defined by recurrence formula +20 Proof of the Hockey-Stick Identity: $\sum_{t=0}^n \binom tk = \binom{n+1}{k+1}$ +15 Prove that the triangles $ABC$ and $AB^{'}C^{'}$ have the same incentre.

### Question (1)

 4 Focus-Focus Definition for a Parabola

### Tags (125)

 84 graph-theory × 40 30 sequences-and-series × 11 48 combinatorics × 29 28 linear-algebra × 15 48 discrete-mathematics × 24 27 calculus × 11 35 elementary-number-theory × 7 24 induction × 5 32 geometry × 28 22 probability × 8

### Accounts (4)

 Mathematics 5,830 rep 719 MathOverflow 897 rep 516 Ask Ubuntu 108 rep 5 Theoretical Computer Science 101 rep 1