2014/067) Show that $\dfrac{1}{n} + \dfrac{1}{n+1} + \dfrac{1}{n+2}$ is a decimal fraction of deferred periodicity

Proof:
above sum is

$\dfrac{3n^2+ 6n + 2 }{n(n+1)(n+2)}$

numerator is not divisible by 3 but denominator is divisible

so it is periodic as 3 is not a factor of 10

again if n id odd then numerator odd but denominator is even so 2 divides denominator but not numerator so it is deferred

if n is even $3n^2+6n$ is divisible by 4 but 2 is not so numerator is not divisible by 4 but denominator is divisible by 4 (actually 8) so in reduced for numerator is odd and denominator is even so if is deferred