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Home / Set $ k = -2 $: $ 1 = B(-2) \Rightarrow B = -rac{1}{2} $.

Set $ k = -2 $: $ 1 = B(-2) \Rightarrow B = -rac{1}{2} $.

February 22, 2026

$Set $ k = -2 $: $ 1 = B(-2) \Rightarrow B = - rac{1}{2} $.$

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Multiply both sides by $ k(k+2) $:
= A(k+2) + Bk.
Set $ k = 0 $: $ 1 = A(2) \Rightarrow A = rac{1}{2} $.
rac{1}{k(k+2)} = rac{1}{2}\left( rac{1}{k} - rac{1}{k+2}
Now substitute into the sum:
\sum_{k=1}^{50} rac{1}{k(k+2)} = rac{1}{2} \sum_{k=1}^{50} \left( rac{1}{k} - rac{1}{k+2}

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