1. ## 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?

2. ## 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}.

3. ## Re: Accumulation Points

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