A dispute that needs end

Khem and Harry have just initiated learning calculus(sequence and series) and while going through problems of exercise they come across with a problem sum to infinity $1-1+1-1+\cdots\cdots$ and while solving the problem they have a dispute .

Khem claims : $\begin{aligned} S & = 1-1+1-1+\cdots \\ & = 1-(1-1+1-1+\cdots) \\ & = 1-S \\ & = \frac{1}{2}\end{aligned}$ Harry claims: $\begin{aligned} S & = 1-1+1-1+\cdots \\ & = (1-1) +(1-1)+\cdots \\ & = 0\end{aligned}$ If you are given to resolve the problem and settle the dispute, whom do you support to be correct?