Answer
$\Sigma_{j=2}^{n-1}\frac{j+1}{j+n}$
Work Step by Step
When i = 3, then j = 2.
When i = n then j = n − 1.
Since j = i − 1, then i = j + 1.
Thus,
$\Sigma^n_{i=3}\frac{i}{i+n-1}=\Sigma^{n-1}_{j=2}\frac{j+1}{(j+1)+n-1}$
=$\Sigma_{j=2}^{n-1}\frac{j+1}{j+n}$
