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We are given the identity: $$ \sum_{i=1}^{n}\frac{1}{i(i+1)} = \frac{n}{n+1} $$ We are to prove this by mathematical induction. --- ### Step 1: Base Case (n = 1) LHS: $$ \sum_{i=1}^{1} \frac{1}{i(i+1)} = \frac{1}{1(1+1)} = \frac{1}{2} $$ RHS: $$ \frac{1}{1+1} = \frac{1}{2} _________ _______ _____ _________ ______ ________ ___ _______ __________ ________ ____.
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