The sum is dominated by the final terms, the initial terms vanishing in the limit.  The final term is 1.  The penultimate term is (1 - 1/n)^n, which becomes exp(-1).  The preceding term is (1 - 2/n)^n, which becomes exp(-2).  So the sum becomes 1 + exp(-1) + exp(-2) + ... = 1/(1 - exp(-1)).   --  Gene On Sunday, December 17, 2017, 1:04:58 PM PST, Dan Asimov <dasimov@earthlink.net> wrote: What is   lim  ((1/n)^n + (2/n)^n + ... + (n/n)^n)   n—>oo (exactly, if possible) ??? My bag of limit tricks doesn't readily seem to include how to solve this one. —Dan