An $\mathrm{e}$ -Like Bound

★ 7/10calculus Monotonicity sequences Estimation Logarithms inequality

Problem

Given $\left(\dfrac{12}{11}\right)^{10} \approx 2.3872$ , prove that for all $n \ge 11$ ,

\left(1 + \frac1n\right)^n < 3\left(1 - \frac1n\right).

Answer

Solution

Difficulty	7/10
Topics	calculus, Monotonicity, sequences, Estimation, Logarithms, inequality

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