Optional extension Factorise $1-\dfrac1{n^2}$, where $n\ne0$. Hence evaluate \(\left(1-\dfrac1{9

Question

Optional extension Factorise $1-\dfrac1{n^2}$, where $n\ne0$. Hence evaluate $\left(1-\dfrac1{9^2}\right)\left(1-\dfrac1{10^2}\right)\cdots\left(1-\dfrac1{15^2}\right)$.

Accepted Answer

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

Telescoping product from a conjugate factorisation

Telescoping product from a conjugate factorisation

Solution:

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