How do you determine if #a_n = (1+1/n^2)^n# converge and find the limits when they exist? Calculus Tests of Convergence / Divergence Strategies to Test an Infinite Series for Convergence 1 Answer Cesareo R. Nov 2, 2017 #lim_(n->oo)a_n = 1# Explanation: #a_n = (1+1/n^2)^n = ((1+1/n^2)^(n^2))^(1/n) # and then #lim_(n->oo) a_n approx lim_(n->oo) e^(1/n) = 1# and the sequence #a_n# converges. Answer link Related questions What is the sum of the series #1+ln2+(((ln2)^2)/(2!))+...+(((ln2)^n)/(n!))+...#? How do I write #(5/(1*2))+(5/(2*3))+(5/(3*4))+...+(5/n(n+1))+...#in summation notation, and how... How do you show whether the improper integral #int ln(x)/x^3 dx# converges or diverges from 1 to... How do you show whether the improper integral #int e^x/ (e^2x+3)dx# converges or diverges from 0... How do you show whether the improper integral #int (79 x^2/(9 + x^6)) dx# converges or diverges... How do you show whether the improper integral #int 1/ (1+x^2) dx# converges or diverges from... How do you prove that the integral of ln(sin(x)) on the interval [0, pi/2] is convergent? How do you show whether the improper integral #int (x^2)(e^(-x^3)) dx# converges or diverges... Using the definition of convergence, how do you prove that the sequence #{5+(1/n)}# converges... Using the definition of convergence, how do you prove that the sequence #{2^ -n}# converges from... See all questions in Strategies to Test an Infinite Series for Convergence Impact of this question 36414 views around the world You can reuse this answer Creative Commons License