I have to find the limits for a whole bunch of sequences and this one has stumped me.
Find the limit as n approaches infinity of n(1 - (1 - (1/n))^(1/k)) where k is a fixed natural number.
Just for clarification, the kth root is around (1 - (1/n)).
I know that the limit is 1/k, but how do you show it algebraically?
Thanks for your help.