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minecraft how to build a bucket - Coaching Toolbox

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 A geometric series has a first term of 3 and a common ratio of 2. Find the sum of the first 5 terms.

📌 The sum \( S_n \) of the first \( n \) terms of a geometric series is given by:

📌 where \( a = 3 \), \( r = 2 \), and \( n = 5 \).

📌 \[ S_5 = 3 \frac{2^5 - 1}{2 - 1} = 3 \times (32 - 1) = 3 \times 31 = 93 \]

📌 Find the derivative of the function \( f(x) = 4x^3 - 5x^2 + x - 7 \).

📌 \[ f'(x) = \frac{d}{dx}(4x^3) - \frac{d}{dx}(5x^2) + \frac{d}{dx}(x) - \frac{d}{dx}(7) \]

📌 \[ f'(x) = 12x^2 - 10x + 1 \]

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