A conducting body 1 has some initial charge $Q$, and its capacitance is $C$. There are two other conducting bodies, 2 and 3, having capacitance: $C_2=2C$  and $C_3\to \infty$  . Bodies 2 & 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

When 2 is touched to 1, charge gets shared between them such that both of them acquire same potential 
$V=\frac{Q_2}{C_2}=\frac{Q_1}{C_1}$
And  $Q_1+Q_2=Q$
$\therefore Q_1=\left(\frac{C_1}{C_1+C_2}\right)Q=\frac{Q}{3}$
Charge acquired by 2 is  $Q_2=\left(\frac{C_2}{C_1+C_2}\right)Q$
When 2 is touched to 3, the entire charge of 2 gets transferred to 3. This is the only way they can have same potential equal to zero.
After first set of  operations, body 1 has $Q_1=\frac{Q}{3}$  charge and the body 2 has no charge. Working similarly, one can see that the change on the body 1 after second set of operations will be  $\frac{Q}{3^2}$.
After N operations, charge on the first body will be  $\frac{Q}{3^N}$.