The following paragraph is from the book CLRS:
Given an ordinary hash function $h' : U \rightarrow \{0, 1, ..., m - 1\}$, which we refer to as an auxiliary hash function, the method of linear probing uses the hash function $h(k, i) = (h'(k) + i) \; \text{mod m}$ for $i = 0, \: 1,\: ... ,\: m - 1$. Given key $k$, we first probe $T[h'(k)]$, i.e., the slot given by the auxiliary hash function. We next probe slot $T[h'(k) + 1]$, and so on up to slot $T[m - 1]$. Then we wrap around to slots $T[0]$, $T[1]$, $...$ until we finally probe slot $T[h'(k) - 1]$. Because the initial probe determines the entire probe sequence, there are only $m$ distinct probe sequences.
Now, in the fourth line I think we should probe $T[(h'(k) + 1) \: \text{mod m}]$ other than $T[h'(k) + 1]$ because we are setting $i = 1$. Actually, if $0 \leqslant h'(k) \leqslant m - 2$, then these two are the same, but if $h'(k) = m - 1$, then they aren't. We simply should iterate over the probe sequence to find an empty slot for insertion but I don't know what's happening here.
