9 Find $\sum_{k=0}^{\infty}\big(\frac{1}{3k+2}-\frac{1}{3k+4}\big)$ 7 Problem of three circles 6 Alternate complex binomial series sum 6 Equilateral triangle that has its vertices on the centers of $3$ different chords of a circle 5 Alternate complex binomial series sum

Reputation (1,405)

 +5 If $d$ divides $a^4+a^3+2a^2-4a+3$, prove that $d$ is a fourth power modulo $13$ +10 Alternate complex binomial series sum +10 Alternate complex binomial series sum +2 Find $\angle BDA$

Questions (4)

 7 If $d$ divides $a^4+a^3+2a^2-4a+3$, prove that $d$ is a fourth power modulo $13$ 5 Prove triangle area formula for barycentric coordinates 4 Find $\sum_{k=0}^{\infty}\big(\frac{1}{3k+2}-\frac{1}{3k+4}\big)$ 2 A rotating polygonal line with increasing side length cannot end up where it started!

Tags (41)

 44 geometry × 17 23 sequences-and-series × 5 32 euclidean-geometry × 10 12 contest-math × 4 30 combinatorics × 11 9 analysis × 2 27 triangles × 6 9 circles × 2 24 summation × 6 9 trigonometry × 2