Need help on series!!!! CAL2?

Question

Find the limits of the following

{1 - 1/n}

How do i approach this question?? thanks a lot !!!!!!!!

Thanks a got it !!!!!

Answer 1

1 - 1/n
when n --> infinity, 1 -1/n --> 1
when n --> -infinity, 1 -1/n --> 1
whne n = 0 , 1-1/n = infinity.

So, the limits of 1 -1/n is
-infinity < n < 0, 0 < n < infinity, n <> 0

Answer 2

A theorem of infinite series says that a series converges if the nth term of the series tends to zero , as n tends to infinity. Here the limit of the nth term is 1 which is not equal to 0. So the series does not converge and consequently the infinite series sigma(1-1/n) is not convergent and does not possess a limit.

Answer 3

i think (-infinity <0< + infinity) hey zero is not included cause it will cause the function to become infinit

Answer 4

refer to Leithold book entitled TC7, you'll find the detailed discussion there..

Answer 5

just let n-->infinity
lim = 1