What is (1+1/2+...1/n)^(1/n)

Question

as n tends to infinity?

Answer 1

The expression is (1+1/2+...1/n)^1/n.

If n tends to infinity, then 1/n tends to zero.

Substitute 0 for 1/n.

=1             [Since anything power zero is 1]

Therefore (1+1/2+...1/n)^1/n = 1 when n = infinity.