gen-in-3-4-sentences-explain-the-limit-of-a-sequence-state-any-k-c1c2

In 3-4 sentences, explain the limit of a sequence. State any key formula.

The limit of a sequence describes the value that the terms of the sequence approach as the index goes to infinity. Formally, we say that a sequence {aₙ} has limit L if the terms aₙ get arbitrarily close to L as n becomes large. **Key formula**: lim(n→∞) aₙ = L means that for every ε > 0, there exists an N such that |aₙ - L| < ε for all n > N. In simpler terms, no matter how small a distance ε we choose, eventually all terms of the sequence stay within that distance of L.