Limits Continuity And Differentiability

If \(a=\lim _\limits{n \rightarrow \infty} \frac{1+2+3+\ldots+n}{n^2}\) and \(b=\lim _\limits{n \rightarrow \infty} \frac{1^2+2^2+3^2+\ldots+n^2}{n^3}\), then