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\textbf{Solution 1: }  (a) Since we are receiving one extra coupon for each consecutive day: $1 + 2 + \ldots + {k-1} (k-1)  + k$, the total coupons received for $k$ days can be represented as $\sum\limits_{i=1}^k i$ = $\frac{k(k+1)}{2}$ \smallskip  \noindent  (b) Since we are still receiving one extra coupon for each consecutive day, $\sum\limits_{i=1}^n i$ can still represent the number of coupons received. However, the value of the coupons is: $1 + 2 + 4 + \ldots+ {n-1} (n-1)  + 2(n-1)$ which can be represented as $\sum\limits_{i=1}^n 2^{n-i}$. \smallskip  We must multiply the quantity and the value together to get the total value resulting in: $W(n) = \sum\limits_{i=1}^n i*2^{n-i}$