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Home » \(A = 1000 \left(1.025\right)^12\) - Baxtercollege

\(A = 1000 \left(1.025\right)^12\) - Baxtercollege

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 This is a telescoping series. Writing the partial sum \( S_N \):

📌 S_N = \left( rac{1}{2} - rac{1}{3}

📌 ight) + \left( rac{1}{3} - rac{1}{4}

📌 ight) + \cdots + \left( rac{1}{N+1} - rac{1}{N+2}

📌 ight) = rac{1}{2} - rac{1}{N+2}

📌 As \( N o \infty \), \( rac{1}{N+2} o 0 \), so:

📌 \lim_{N o \infty} S_N = rac{1}{2}

📌 The series converges to \( rac{1}{2} \).

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