1.
If a=limn1+2+3++nn2a=\displaystyle\lim_{n\to\infty}\frac{1+2+3+\ldots+n}{n^2} and b=limn12+22++n2n3b=\displaystyle\lim_{n\to\infty}\frac{1^2+2^2+\ldots+n^2}{n^3}, then