Evaluate [tex]\displaystyle\lim_{n\to\infty}\sum^{n}_{i=1}3\left(1+\dfrac{i}{n}\right)^{2}\dfrac{1}{n}.[/tex] #Challenge
In ascending order, each positive number [tex]n[/tex] appears [tex]n[/tex] times in a sequence [tex]a_{n}[/tex]. [tex]\text{$1, 2, 2, 3, 3, 3, 4, 4, 4, 4, \cdots.$}[/tex] Find the following value. [tex]\Huge\text{$\rightarrow\displaystyle\sum^{7}_{k=1}a_{10^{k}}.$}[/tex] #Challenge