Exercise 6, § 3

Let k be a field and A the ring of formal series k[[X_1, X_2]]. Consider an ideal n of A containing a power of the maximal ideal m of A, and the ideal I generated by (X_1 − X_2).n, M the A-module A/I. Prove that the sequence (X_1) is secant for M without being completely secant for M.