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 $$\lim_{n\to\infty} \sum_{i=1}^{n}\frac{16(n+i)}{n^2}.$$