Using the method of Example 2.2i, prove that the following limit exists. (2n2+1)/(3n2)2/3asn. EXAMPLE 2.2 i) Prove that 10 as n. Proof. i) Let >0. Use the Archimedean Principle to choose NN such that N>1/. By taking the reciprocal of this inequality, we see that nN implies 11/N<. since are all positive it follows that for nn>