Question
Prove that for every positive integer $n$,$$1 \cdot 2+2 \cdot 3+\cdots+n(n+1)=n(n+1)(n+2) / 3 .$$
Step 1
Base Case (n=1): For n=1, the left side of the equation is 1(1+1) = 2, and the right side is 1(1+1)(1+2)/3 = 2. Since both sides are equal, the statement holds true for n=1. Inductive Step: Assume the statement is true for n=k, i.e., 1⋅2 + 2⋅3 + ... + k(k+1) = Show more…
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