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Home » $ e^-2 \approx 0.135 $ - Redraw

$ e^-2 \approx 0.135 $ - Redraw

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 However, double-check: maybe \( a=3, d=2 \), \( S_n = \frac{n}{2}[6 + (n-1)2] = \frac{n}{2}(2n + 4) = n(n+2) \).

📌 Set \( n(n+2) = 210 \), \( n^2 + 2n - 210 = 0 \), \( n = \frac{-2 \pm \sqrt{4 + 840}}{2} = \frac{-2 \pm \sqrt{844}}{2} \).

📌 \( \sqrt{844} = 2\sqrt{211} \approx 29.0526 \), so \( n \approx \frac{27.0526}{2} \approx 13.526 \). Not integer.

📌 But since number of terms must be integer, and 210 is not achievable, perhaps the problem has a typo.

📌 However, for the sake of the exercise, assume the equation is correct and solve: no integer, but closest is not valid.

📌 But let’s assume the intended answer is \( n = 14 \) with corrected sum — but it doesn’t match.

📌 Alternatively, perhaps the sum is 195? But problem states 210.

📌 After re-evaluation, realize: the problem may expect solving the quadratic and taking positive root: \( n = \frac{-2 + \sqrt{844}}{2} \approx 13.525 \), but not integer.

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