## there exist infinite many n∈Nn\in\mathbb{N} such that Sn−[Sn]<1n2S_n-[S_n]<\frac{1}{n^2}

Let Sn:=1+12+13+…+1n. Is it true that the set of n∈N such that Sn−[Sn]<1n2 is infinite? Here, [x] represents the largest integer not exceeding x. This question has been asked previously on math.SE without receiving any answers. Answer AttributionSource : Link , Question Author : math110 , Answer Author : Community