How do you find the Limit of #n^( ln( (n+1)/n )# as n approaches infinity? Calculus Limits Determining Limits Algebraically 1 Answer A. S. Adikesavan Jan 10, 2017 1 Explanation: Use #(ln n)/n^k to 0#, as# n to oo, k = 1, 2, 3, .. # Let #f = n^(ln((n+1)/n)=n^(ln(1+1/n))#. #log f = ln(1+1/n)ln n# #=ln n(1/n-1/(2n^2)+1/(3 n^3)..# #to 0-0+0-...,#, (alternately #0 and -0)# as #n to oo#. So, #ln f to 0 and f to1 #.. . Answer link Related questions How do you find the limit #lim_(x->5)(x^2-6x+5)/(x^2-25)# ? How do you find the limit #lim_(x->3^+)|3-x|/(x^2-2x-3)# ? How do you find the limit #lim_(x->4)(x^3-64)/(x^2-8x+16)# ? How do you find the limit #lim_(x->2)(x^2+x-6)/(x-2)# ? How do you find the limit #lim_(x->-4)(x^2+5x+4)/(x^2+3x-4)# ? How do you find the limit #lim_(t->-3)(t^2-9)/(2t^2+7t+3)# ? How do you find the limit #lim_(h->0)((4+h)^2-16)/h# ? How do you find the limit #lim_(h->0)((2+h)^3-8)/h# ? How do you find the limit #lim_(x->9)(9-x)/(3-sqrt(x))# ? How do you find the limit #lim_(h->0)(sqrt(1+h)-1)/h# ? See all questions in Determining Limits Algebraically Impact of this question 5720 views around the world You can reuse this answer Creative Commons License