OmG

 12 why area of triangle changes when measured as components of triangles? 6 Show that $4^{3x+1} + 2^{3x+1}+ 1$ is divisible by 7 5 Why is $\prod_{k=n}^{2n-3}\left(2n-k\right) = \prod_{j=3}^{n}j$? 4 Realistic 3D fractal Christmas tree 4 why is $\frac{k\cdot n!}{k!(n-k)!} = \frac{n(n-1)!}{(k-1)!((n-1)-(k-1))!}$?

### Reputation (2,648)

 +35 How do I prove that this recurrence relation is O(n^2) +8 How to define quantity of real roots? +20 Show that the vectors $v_1 = \begin{pmatrix} 1 \\ 2 \end{pmatrix}$ and $v_2 = \begin{pmatrix} 2 \\ 3 \end{pmatrix}$ are linearly independent… +10 Understand $E[X^2]$ in probability variance

### Questions (3)

 0 Minimum alpha for the following inequality 0 Is there any recursive relation 0 $\frac{\int_0^1x^n\sqrt{1-x^2}}{\int_0^1x^{n-2}\sqrt{1-x^2}}$ [duplicate]

### Tags (129)

 19 sequences-and-series × 15 12 linear-algebra × 9 16 discrete-mathematics × 17 10 algebra-precalculus × 8 16 elementary-number-theory × 7 10 limits × 4 16 geometry × 5 9 number-theory × 7 15 triangles × 3 9 contest-math × 2