1. show that ∞Σ n=1 (1/n^2) converges(use the monotone convergence theorem)

2. show that a decreasing sequence that is bounded from below converges to the infimum of its range.

3. let (An)上∞下n=1 be a sequence and let L ∈ R suppose that (An)上∞下n=1 does not converge to L show that there is an ∈>0 and a subsequence (Ank)上∞下k=1 of (An)上∞下n=1 such that ∥ank-L∥≧∈ for all k∈N

please step by step