Question
Use mathematical induction to prove that the formula is true for all natural numbers $n$.$$1 \cdot 2+2 \cdot 3+3 \cdot 4+\dots+n(n+1)=\frac{n(n+1)(n+2)}{3}$$
Step 1
The left hand side of the equation becomes $1 \cdot 2$ and the right hand side becomes $\frac{1 \cdot(1+1) \cdot(1+2)}{3}$. Since both sides are equal, the base case holds. Show more…
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