Solution: Share a solution. Let un= 1/√[n(n? - 1)]，vn= 1/√n？ ,∴lim(n→∞)un/vn=lim(n→∞)√[n？ /(n？ - 1)]= 1。
∴ Series∴ UN and∴ VN have the same convergence and divergence. And ∑vn is p = 3/2 >；; P series of 1, convergence. ∴ series ∑1√ [n (n? -1)] convergence.