Hint :
Set
and show :
lim n→∞ (n^(1/n)+1) = lim n→∞ (n^(1/n)) +1
lim n→∞ (n^(1/n)) is indeterminate, use L'Hopital's Rule
First change the limit into e^(lim n→∞ ln(n^(1/n))) = e^(lim n→∞ (1/n)*ln(n))
(1/n)*ln(n) = ∞/∞, take derivative of the numerator and the denominator
e^(lim n→∞ (1/n)) = 1
lim n→∞ (n^(1/n)+1) = 1+1 = 2