
Accumulation Points
I am trying to find the set of accumulation points of the subset of the real numbers.
{(1)^n*(1+1/n): n is an element of the natural numbers}
I plugged in values for n to find a pattern and got the following results:
n=1: 2
n=2: 3/2
n=3: 4/3
n=4: 5/4
n=5: 6/7
n=6: 7/6
n=7: 8/7
n=8: 9/8
The values are negative when n is odd and positive when n is even. They begin to accumulate around 1 and 1, but not every point is represented. Does that mean the set of accumulation points is the empty set?

Re: Accumulation Points
I'm not sure what you mean by "not every point is represented" but how can you say "they begin to accumulate around 1 and 1" and suggest that there are no accumulation points? For all even n, the subsequence is (1+ 1/n) which obviously converges to 1. For all odd n, the subsequence is (1+ 1/n) which obviously converges to 1. The set of accumulation points is {1, 1}.

Re: Accumulation Points
I realized after I posted that I contradicted myself. However, by doing so, I understand why those are the accumulation points.