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A compound-interest limit in disguise

EasyCalculus~3m

Evaluate lim⁡n→∞(n+2n−1)n\lim_{n\to\infty}\left(\dfrac{n+2}{n-1}\right)^{n}. (to 3 decimals)

Show hints (2)+
  1. Rewrite the base as 1+3n−11 + \tfrac{3}{n-1}.
  2. Match the exponent to n−1n-1; the limit is e3e^{3}.

Answer

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20.086 (± 0.02)

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Asked at: Timed Mental-Math & Sequences, Game-Based Aptitude

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