Telescoping product from a conjugate factorisation

Telescoping product from a conjugate factorisation

Secondary 2
TGM Original Questions
  1. Factorise \(1-\frac1{n^2}\) completely.
  2. Hence evaluate \(\displaystyle\prod_{n=9}^{15}\left(1-\frac1{n^2}\right)\).

Solution:

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Answer:(a) \(\frac{(n-1)(n+1)}{n^2}\); (b) \(\frac{128}{135}\).

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