Dat Do edited beginproblem_a_You_a.tex  about 10 years ago

Commit id: 5844105216c7da71efd1144c6565c7fcd661f236

deletions | additions      

       

\smallskip  \noindent  (b) Since we are still receiving one extra coupon for each consecutive day, $\sum\limits_{i=1}^k $\sum\limits_{i=1}^n  i$ can still represent the number of coupons received. However, the value of the coupons is: $1 + 2 + 4 + 8 + \ldots + 2{n-1}$ 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: $W(n) = \sum\limits_{i=1}^n i*2^{n-i}$  \smallskip  \noindent  (c) $W(n) = \sum\limits_{i=1}^n i*2^{n-i} = 2^{n+1}-n-2$  \begin{problem}