9

Part of 1950 Miklós Schweitzer

Problems(2)

Miklos Schweitzer 1950_9

Source: first round of 1950

Find the sum of the series x\plus{}\frac{x^3}{1\cdot 3}\plus{}\frac{x^5}{1\cdot 3\cdot 5}\plus{}\cdots\plus{}\frac{x^{2n\plus{}1}}{1\cdot 3\cdot 5\cdot \cdots \cdot (2n\plus{}1)}\plus{}\cdots

calculusreal analysisreal analysis unsolved

Miklos Schweitzer 1950_9

Source: second part of 1950

Find the necessary and sufficient conditions for two conics that every tangent to one of them contains a real point of the other.

conicsreal analysisreal analysis unsolved