Problem - 3928
John uses the equation method to evaluate the following expression:$$S=1-1+1-1+1-\cdots$$ and get $$S=1-S \implies \boxed{S=\frac{1}{2}}$$
However, $S$ clearly cannot be a fraction. Can you point out what is wrong here?
The given expression does not converges to a fixed finite value. Therefore, the equation method cannot be used. See Evaluate Infinite Expression.