Analyzing aₙ = n/(n+1)

Calculus 2 · Axiom Academy

Compute terms, visualize the behavior, conjecture the limit, and prove it with limit laws Consider the sequence . Compute its first terms, look at how they behave, conjecture the value of , and then prove that limit rigorously using limit laws. Nice work — you analyzed a sequence from three angles and tied them together. Here is what we used: Computational approach: evaluating specific terms ( ) gives concrete numerical evidence for the limit. Graphical approach: plotting the terms on a number line shows the convergence behavior at a glance. Algebraic manipulation: rewriting as exposes the limit structure. Rigorous proof: the quotient law plus turns the conjecture into a proof. Conjecture from computation and visualization, then prove algebraically — a reliable strategy for analyzing sequences and their limits throughout calculus.

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