Mystery of Infinity-2
Number Theory
Level
2
We all know the famous identity:
\(0.9999\ldots{ }\ldots{ }\ldots = 1\).
Here the numbers on the both sides are in base \(10\).
One special thing here about \(9\) is: in this case, \(9\) just one less than the base \(10\).
So, noticing this special property, one can make the conjecture that
The equality \(0.ccc\ldots{ }\ldots{ }\ldots = 1\) is true in every base \(b \geq 2\), where \(c\) is the largest digit in base \(b\), equivalently, \(c=b-1\).
Is this conjecture TRUE?
by
Muhammad Rasel Parvej