The following expression
$\lim_{n\to\infty} \sum_{i=1}^{n} \frac{4}{n}\cdot \frac{4+4i}{n}$
can (according to the book I'm reading, and I'm sure it's correct) be simplified to
$\lim_{n\to\infty} \sum_{i=1}^{n}\frac{16(n+i)}{n^2}.$
Where is the numerator $n$ coming from? Looking at it it seems like it should simplify to
$\lim_{n\to\infty} \sum_{i=1}^{n}\frac{16(1+i)}{n^2}$
What painfully obvious fact am I ignoring?
UPDATE
In hindsight (and with the answers here) I believe it is a typo, but should in fact read
$\lim_{n\to\infty} \sum_{i=1}^{n} \frac{4}{n}\cdot \Big( 4+ \frac{4i}{n} \Big)$
Which does simplify to $\lim_{n\to\infty} \sum_{i=1}^{n}\frac{16(n+i)}{n^2}.$