Thread: 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?

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}.

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