I'm working through some sample problems in preperation for a test... and I'm confused about something.
I'm given the series Sum of e^(1/n) - 1. I went through the example... then looked at the correct answer and it showed this:
lim n approaches infinity of e^(1/n) - 1/ 1/n = 1.
So, of course they compared the first term to 1/n, which is a diverging P series. But, when you take the limit as n approaches infinity, 1/n goes to zero. So, you e^0 (which is one) - 1 = 0 divided by 1/n which is 0. So, you should get 0/0... which is zero... isnt it?
I'm given the series Sum of e^(1/n) - 1. I went through the example... then looked at the correct answer and it showed this:
lim n approaches infinity of e^(1/n) - 1/ 1/n = 1.
So, of course they compared the first term to 1/n, which is a diverging P series. But, when you take the limit as n approaches infinity, 1/n goes to zero. So, you e^0 (which is one) - 1 = 0 divided by 1/n which is 0. So, you should get 0/0... which is zero... isnt it?
