Question

Could you please explain how the series, 1/(n-1) is divergent and not convergent to zero?

Answer 1

it does converge to zero. divide 1 by positive numbers, and it gets smaller as the divisor is increased. It is always positive, and it can be made as small as you want by picking increasingly larger numbers, which happens as n goes to infinity. It converges to zero.

Answer 2

Type: limit as n goes to infinity 1/(n-1)

into http://www.wolframalpha.com

Answer 3

http://www.wolframalpha.com/input/?i=is+1%2F%28n-1%29+convergent

Apparently, when I ask if it's convergent, then it comes out as false.

Answer 4

Oh, whoops. I forgot that a sequence and a series are different things. You can use the ratio test to show that it doesn't converge. Read this http://en.wikipedia.org/wiki/Ratio_test and see that a(n+1) / a(n) is always greater than one. According to the ratio test, that means that the series diverges. Maybe you can read more about the ratio test to see why that tells you it diverges.

Answer 5

oh alright, i'll read up on that by myself. thanks for sticking with me! >_<;