A conducting body $1$ has some initial charge $Q$, and its capacitance is $C$. There are two other conducting bodies, $2$ and $3$, having capacitances : $C_2 = 2C$ and $C_3 \rightarrow \infty$ . Bodies $2 $ and $3 $ are initially uncharged. "Body $2$ is touched with body $1$. Then, body $2$ is removed from body $1 $ and touched with body $3$, and then removed." This process is repeated $N$ times. Then, the charge on body $1$ at the end must be
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