Prove: Let un= 1/n, ∴ lim (n →∞) UN = lim (n →∞)1/n = 0.

Furthermore, un-(un+1) =1/n-1(n+1) =1[n (n+1) > 0, ∵ (un+ 1). Therefore, the staggered series ∑ [(- 1) n]/n satisfies the conditions of Leibniz discriminant method.

∴∑ [(- 1) n]/n convergence.

For reference.