Limits Continuity And Differentiability

If N = n! (n \(\in\) N, n > 2), then find \(\mathop {\lim }\limits_{N \to \infty } \left[ {{{({{\log }_2}N)}^{ - 1}} + {{({{\log }_3}N)}^{ - 1}} + \,\,.....\,\, + {{({{\log }_n}N)}^{ - 1}}} \right]\).