$(6)$ Assume you could save $\backslash (\backslash$$ $1\backslash )$ on September $1$st$,\backslash (\backslash$$ $2\backslash )$ on September $2$nd$,\backslash (\backslash$$ $4\backslash )$ on September $3$rd$,$ and $\backslash (\backslash$$ $8\backslash )$ on the $4$ th and so on$.$

$($a$)$ What is the amount you will save on September $30$th$?$

$($b$)$ What would be the total amount of your saving during the month of September.