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