Show that the sequence P_n = [(n+1)/n, [(-1)^n]/n] converges.
A sequence p_n converges to a point p if and only if every neighborhood about p contains all the terms p_n for sufficiently large indices n; to any neighborhood U about p, there corresponds an index N such that p_n exists in U whenever n > or = N.
The Attempt at a Solution
The sequence converges to the point p = (1 0). Let U be the open ball around p with radius r>0. Need to show that |p_n - p|< r for all n > or = N i.e. ....
|((n+1)/n, ((-1)^n)/n) - (1, 0)| < r
sqrt of ((n+1)/n - 1)^2 + (((-1)^n)/n)^2 < r
Now I assume the n and N come into play, but I don't know how.