this is for holding javascript data
Dat Do edited beginproblem_a_You_a.tex
about 10 years ago
Commit id: 685c1e94fd46329112dd955e0a424695f43643a6
deletions | additions
diff --git a/beginproblem_a_You_a.tex b/beginproblem_a_You_a.tex
index 8bf1f74..777f682 100644
--- a/beginproblem_a_You_a.tex
+++ b/beginproblem_a_You_a.tex
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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: $W(n) = \sum\limits_{i=1}^n i*2^{n-i}$