We will use induction to prove that $1+2+3+\cdots+n = \frac{n(n+1)}{2}$ for every positive integer $n$.
Base case: For $n=1$, we have $1 = \frac{1(1+1)}{2} = 1$, which is true.
Inductive step: Assume the statement is true for some positive integer $k$, i.e.,
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