SEAMO 2027 - Paper E - SET 09 - Self-study Question 21

Question 21

Let $n$ be a positive integer. Evaluate $$\begin{aligned}&1+\left(\frac12+\frac22+\frac12\right)+\left(\frac13+\frac23+\frac33+\frac23+\frac13\right)\\&\quad+\cdots+\left(\frac1n+\frac2n+\cdots+\frac nn+\frac{n-1}{n}+\cdots+\frac1n\right).\end{aligned}$$

$\frac{n(n+1)}2$
$\frac n2$
$\frac{n+1}2$
$n$
None of the above