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Estimating Pi with Leibniz Series

Hard · Mental Math & Estimation · Quant Trader interview question · mental-math, estimation, series, pi

You're interviewing for a quantitative trading role. The interviewer asks you to estimate the value of $\pi$ using the first four terms of the Leibniz series for $\pi/4$: $\frac{\pi}{4} \approx 1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7}$. Provide your best mental estimate of $\pi$ based on this approximation. You are not allowed to use a calculator.