Convergence and divergence of sequences
General · Mathematics
Study notes
Q: Prove 1/n → 0 with ε. Does (-1)ⁿ converge? Given ε > 0: n > 1/ε gives |1/n - 0| = 1/n < ε ✓. CONVERGES to 0! (-1)ⁿ: -1, 1, -1, 1...: never settles - DIVERGES (oscillates!). Two subsequences → different limits (-1, 1): can't converge!