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\fracn!k_1! \cdot k_2! \cdots k_m! - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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We apply partial fraction decomposition:
rac{1}{(n + 1)(n + 2)} = rac{A}{n + 1} + rac{B}{n + 2}
Multiplying both sides by \((n + 1)(n + 2)\):
= 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:

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