Determine if the sequence converges or diverges

Question

a_n=(1+(1/n³))^n

Answer 1

As n goes to positive infinity (+∞), (1 + 1/n³) goes to (1 + a tiny fraction that is zero for all practical purposes). Then lim_(n→+∞)(1 + 1/n³)ⁿ equals lim_(n→+∞)(1)ⁿ or 1 and the sequence converges to 1.