Let $L/K$ be an extension of number fields, $M_K, M_L$ complete sets of representatives of places at $K$ and $L$, respectively. I'm familiar with the formula:
$$\sum_{w\in M_L, \,\,w|v} n_w=[L:K]n_v\,\,\,\,\text{ for every }v\in M_K$$
However, I've read in a textbook that the result below could be deduced from the formula:
$$\sum_{v\in M_K, \,\,v\text{ archim.}} n_v=[K:\mathbb{Q}]$$
I can't see why this is so.