Λόγος ST

Αν

$$S={\displaystyle \frac{1}{1\cdot 2}}+{\displaystyle \frac{1}{3\cdot 4}}+...+{\displaystyle \frac{1}{99\cdot 100}}$$

$T={\displaystyle \frac{1}{51\cdot 100}}+{\displaystyle \frac{1}{52\cdot 99}}+...+{\displaystyle \frac{1}{99\cdot 52}}+{\displaystyle \frac{1}{100\cdot 51}}$

να βρεθεί ο λόγος  ${\displaystyle \frac{S}{T}}$.