Number Theory, Advanced Algebra & Olympiad Geometry question bank (Mathematical Reasoning & Achievers Section)

Olympiad Geometry: In a cyclic quadrilateral $ABCD$ in 'Number Theory: Primes, Divisibility Rules, Modular Arithmetic and Cryptarithms', the side lengths are $AB = 2, BC = 3, CD = 4, DA = 5$. By Ptolemy's Theorem, the product of diagonals $AC \cdot BD$ is:

Algebraic Telescoping: In 'Number Theory: Primes, Divisibility Rules, Modular Arithmetic and Cryptarithms', evaluate the product: $P = \left(1 - \frac{1}{4}\right)\left(1 - \frac{1}{9}\right)\left(1 - \frac{1}{16}\right) \dots \left(1 - \frac{1}{100}\right)$: