Any occurrence of the variable x which appears in R or P is said to be in the scope of the quantification over x. An occurence of x which is in the scope of a quantification over x is said to be a bound occurrence. An occurence of a variable x which is not in the scope of any quantification over x is said to be a free occurrence.
If the variable x does occur free in the expression P we write
x dnof in P, or following the text, Ø occurs(`x¢,`P¢).
Look at

The k's which appear in 1 £ k £ 6 and k^{2} are in the scope of the quantification over k and are bound occurrences of k. The k which appears to the left of the + is not in the scope of any quantification over k and is a free occurrence of k.
You can see that the k's are different by considering
k+(+k  1 £ k £ 6:k^{2}) for universe of
discourse N. We obtain
and the freely occurring k is the only occurrence of k which remains.
k+(1^{2} + 2^{2} + 3^{2} + 4^{2} + 5^{2} + 6^{2})