Induction · Challenge problem

"Claim": $1 + 2 + \cdots + n = \dfrac{(n + \tfrac12)^2}{2}$. The step really works (adding $k + 1$ to $\dfrac{(k + \frac12)^2}{2}$ gives $\dfrac{(k + \frac32)^2}{2}$), but the base fails. By how much does the claimed formula exceed the true sum at $n = 100$?