Sequence Convergence Guide
Does the sequence converge? Test classic families — powers, geometric, the e-limit, factorials.
A sequence converges if its terms home in on one finite number as n → ∞.
① Answer
② Steps
③ Why it works
Convergence is about eventual behavior: do the terms settle down? The workhorses: 1/np → 0 (p > 0); rn → 0 only when |r| < 1 (each step shrinks); (1+r/n)n → er (the compound-interest limit); and n!/nn → 0 because n!/nn ≤ 1/n — the denominator wins by a factor of n.