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\textbf{Solution 1: }  (a) Since we are receiving one extra coupon for each consecutive day, day: $1 + 2 + \ldots + k$,  the total coupons received for $k$ days can be represented as $\sum\limits_{i=1}^k i$ = $\frac{k(k+1)}{2}$ \smallskip  \noindent