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Home » His Mercies Are New Every Morning—This Miraculous Transformation Will Blow Your Mind! - Crankk.io

His Mercies Are New Every Morning—This Miraculous Transformation Will Blow Your Mind! - Crankk.io

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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\( 1 = B(-1) \Rightarrow B = -1 \)
Setting \( n = -1 \):
\( 1 = A(1) \Rightarrow A = 1 \)
rac{1}{(n + 1)(n + 2)} = rac{1}{n + 1} - rac{1}{n + 2}
The series becomes:
\sum_{n=1}^{\infty} \left( rac{1}{n + 1} - rac{1}{n + 2}
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}

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