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Home » From Scared to Confident: How Doctor Teeth Transformed Smiles Across the City! - Carbonext

From Scared to Confident: How Doctor Teeth Transformed Smiles Across the City! - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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= A(n + 2) + B(n + 1)
Setting \( n = -2 \):
\( 1 = B(-1) \Rightarrow B = -1 \)
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}

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