Question

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

Answer 1

sum of n natural numbers = n(n+1)/2

sum of sauares of n natural number is n(n+1)(2n+1)/6