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Home » $ 72 = 2^3 \cdot 3^2 $ - AssociationVoting

$ 72 = 2^3 \cdot 3^2 $ - AssociationVoting

📅 May 15, 2026 👤 scraface

May 15, 2026

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\frac{1}{k(k+1)} = \frac{A}{k} + \frac{B}{k+1}
Solving \( 1 = A(k+1) + Bk \), we equate coefficients:
\( A + B = 0 \)
\( A = 1 \)
Thus, \( B = -1 \). So,
The series becomes telescoping:
All intermediate terms cancel, leaving:
- \frac{1}{51}
= \frac{51 - 1}{51} = \frac{50}{51}
Thus, the sum is \(\boxed{\frac{50}{51}}\).

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