Can Infinity be One [part 2]

Algebra Level 4

Let the two values of x be a and b such that a> b then find the value of a(a-b)

1 solution

Akshat Sharda
Sep 29, 2015

$\Rightarrow 0.nnnn\ldots \infty=\frac{n}{9}$

$\Rightarrow \frac{\displaystyle \prod^{x}_{n=1}\left(\frac{n}{9}\right)}{\displaystyle \prod^{8}_{n=1}\left(\frac{n}{9}\right)}=1$

$\Rightarrow \displaystyle \prod^{x}_{n=1}\left(\frac{n}{9}\right)=\displaystyle \prod^{8}_{n=1}\left(\frac{n}{9}\right)$

$x\Rightarrow$ $a=9$ and $b=8$ .

$\Rightarrow a(a-b)=9(9-8)=\boxed{9}$